Problem 53995. Solve an ODE: nonlinear third-order equation

Created by ChrisR

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Write a function to solve the ordinary differential equation</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/><w:attr w:name=\"altTextString\" w:val=\"y'y'' = y'''\"/></w:customXmlPr><w:r><w:t>y\\prime y\\prime\\prime = y\\prime\\prime\\prime</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>on the domain </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"0 &lt;= x &lt;= 1\"/></w:customXmlPr><w:r><w:t>0 \\le x \\le 1</w:t></w:r></w:customXml><w:r><w:t> with </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"y(0) = y0\"/></w:customXmlPr><w:r><w:t>y(0) = y_0</w:t></w:r></w:customXml><w:r><w:t>, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"y(1) = y1\"/></w:customXmlPr><w:r><w:t>y(1) = y_1</w:t></w:r></w:customXml><w:r><w:t>, and either </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"y'(0) = y'0\"/></w:customXmlPr><w:r><w:t>y\\prime(0) = y\\prime\n_0</w:t></w:r></w:customXml><w:r><w:t> or </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"y''(0) = y''0\"/></w:customXmlPr><w:r><w:t>y\\prime\\prime(0) = y\\prime\n\\prime_0</w:t></w:r></w:customXml><w:r><w:t>. The input variable </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>ord</w:t></w:r><w:r><w:t> indicates the order (either 1 or 2) of the specified derivative. The function should return the values of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"y(x)\"/></w:customXmlPr><w:r><w:t>y(x)</w:t></w:r></w:customXml><w:r><w:t> at the requested values of the independent variable </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"x\"/></w:customXmlPr><w:r><w:t>x</w:t></w:r></w:customXml><w:r><w:t>.</w:t></w:r></w:p></w:body></w:document>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 124px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 62px; transform-origin: 407.5px 62px; vertical-align: baseline; "><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 176.35px 7.66667px; transform-origin: 176.35px 7.66667px; unicode-bidi: normal; "><span style="">Write a function to solve the ordinary differential equation</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="vertical-align:-5px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAI4AAAAkCAYAAABfegKAAAAEYElEQVR4Xu1bOYsWQRDd/QkekRh5BEaKKCYaGHklgoKKIAbiFRiJogYGoqJoIuIBBpuICoKRogYaaCIaaGTgERp54C/Q92BqaXr7m+7pr3q+GrYHHgvf9FR3v3pTXdU9Oz1Vr8pABgPTGc/URyoDU1U4VQRZDFThZNFWH6rCqRrIYqAKJ4u2+lBp4TwHxSuADcCvAnTH7C9Dny+BD8DeAv1bNanByylM7gqwBvjkT7SkcFajs4/AH2BlAeGk2D+Cfu8AL4CtVr2sPC4tXn5jXAuATcDbPoVzEZ2dBS4B55TJobkU++/Rbh2wA3hWYAwWTWrwsh0TewowUq8PTbJkxPmKDhc2jvtegOGYfS5T39omX2BMFkxq8HILEznW9sKVEo44rVS0SbHPnObBPIs2WrxQfEwxgtGGb0cp4TC3uFww2qTYf4j+l7dN3kJ4UB6DBi+SI7Uu76WEw6z+CXBXmRgxl2L/HxoHK4JCY7JgVoMXVlNrgdYqNEU4i2BkFfAZ8EtqhsYl3j22fwd0KcE3ov0PwM+FpG/3Xop9JncHYpO34OnIGCbBCwuKQ8CcEtwd6yjhcMDbACZILMl4HQ1EECnZWO7ub4RFx1I0bVUMBbcbOAxwOeH1KOBoLjd7AK63rI4orFT7FPScMjLiKLktgk1sPrJZ6GVos2mBF0Ya8t56xSKOvN10LisUP4pI9s1OFjfCifXp3xdx8Hd/aZEEl/f6LKn54rzpOpFA+9DLlmrWIi+zY48Jhw1d54U2gygeZt8jM/AIU1IJsNlp4KrXXvrPFWaqo9x2TBC5azrudQMGcvePLPLSSTiMOj+bJ0LlNTec/gYc3oV02agLbTgxXzkBzJedX5c3s7ykRBxORMImHUsHukkya/5dQGsyFVGRHA2wGZdFN0lmRKPtUhVaF4H33dYsL6nCcSfg5iFcRnYC4x4gyt4BHePmBQzXFCt3oOfjZZaXVOG4E9jXRCA6UiPaiCCkQruNH443P04q2kyqqgq9HJZ4mR1fqnD4gD8BRqHNCtFGBuMvh0tx4/WEoo2FqsoiL1nC8R37BVZkb0VjGXGXQ1ZQ94EZJ7pp9JFqw0JVJWO1xEuWcGQC3Izjx1Hc19H8XMJdDrlcjVPipwpkCO1M8tJlqXLDN0XDL/u0L54vyeVXV9p9DcmeOV66CIdEywRK7eLykG4LUOpzjCGJxR2rOV5yhONWPdqOkG9lS0Qz7bH2ac8cL12Ew6VqptASRSewBNZOuPt0bqm+TPKSKhzZiNOsonyiub1+HYiezJbykFG7JnlJEQ4Vz1B5Hsg9sIv5hBt9rNY0q7RYn0O4b5aXkHB4fHAQeAU8BvidzD1A66xI9kh4HnUNOAnwSGHcY4shCKFtjIPiJSQcyeBlku4Rg4Zz5B+9xFbJZFtjvH3ZGBQvIeFQ+WcAHjEwImj/awuXvgtNlLmJv7lf6fXl0L76GRQvKTlOX8TVfgbEQBXOgJxlaahVOJa8MaCx/Ac8ViI0v+/5OwAAAABJRU5ErkJggg==" alt="y'y'' = y'''" style="width: 71px; height: 18px;" width="71" height="18"></span></div><div style="block-size: 64px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 32px; text-align: left; transform-origin: 384.5px 32px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 46.2917px 7.66667px; transform-origin: 46.2917px 7.66667px; unicode-bidi: normal; "><span style="">on the domain </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" alt="0 <= x <= 1" style="width: 62.5px; height: 18px;" width="62.5" height="18"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16.3333px 7.66667px; transform-origin: 16.3333px 7.66667px; unicode-bidi: normal; "><span style=""> with </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" alt="y(0) = y0" style="width: 60px; height: 20px;" width="60" height="20"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.66667px; transform-origin: 3.88333px 7.66667px; unicode-bidi: normal; "><span style="">, </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" alt="y(1) = y1" style="width: 60px; height: 20px;" width="60" height="20"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 36.95px 7.66667px; transform-origin: 36.95px 7.66667px; unicode-bidi: normal; "><span style="">, and either </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" alt="y'(0) = y'0" style="width: 70px; height: 20px;" width="70" height="20"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.1083px 7.66667px; transform-origin: 10.1083px 7.66667px; unicode-bidi: normal; "><span style=""> or </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" alt="y''(0) = y''0" style="width: 78.5px; height: 20px;" width="78.5" height="20"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 61.4583px 7.66667px; transform-origin: 61.4583px 7.66667px; unicode-bidi: normal; "><span style="">. The input variable </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.55px 7.66667px; transform-origin: 11.55px 7.66667px; unicode-bidi: normal; "><span style="font-family: Menlo, Monaco, Consolas, &quot;Courier New&quot;, monospace; perspective-origin: 11.55px 8px; transform-origin: 11.55px 8px; ">ord</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.5083px 7.66667px; transform-origin: 31.5083px 7.66667px; unicode-bidi: normal; "><span style=""> indicates the order (either 1 or 2) of the specified derivative. The function should return the values of </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" alt="y(x)" style="width: 30px; height: 18.5px;" width="30" height="18.5"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 84.4px 7.66667px; transform-origin: 84.4px 7.66667px; unicode-bidi: normal; "><span style=""> at the requested values of the independent variable </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">x</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.66667px; transform-origin: 1.94167px 7.66667px; unicode-bidi: normal; "><span style="">.</span></span></div></div></div>

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Problem 53995. Solve an ODE: nonlinear third-order equation

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