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How to customize a complex differentiated equation?

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Sherwin
Sherwin 2022-4-8
评论： Sherwin 2022-4-8
I have an equation as s = diff(Z,u)= sqrt((r^2+e3*G*H*x^4e2-f^3*b)/(c^7+r*x*w*p));
I want to put this equation (diffrentiated term) equal to 0 and get x (x on one side and everything else on the other side). x is the only variable in this equation and the rest are parameters. How can I do that in MATLAB?

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Torsten
Torsten 2022-4-8
The term is 0 if r^2+e3*G*H**x^4e2-f^3*b = 0. Can you solve for x ?
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Walter Roberson
Walter Roberson 2022-4-8
diff(Z, u) is independent of x, so you can replace that term by a variable.
Now multiply both sides by the denominator, getting a polynomial in x on one side and square root of a polynomial on the other. square both sides to get a polynomial in x and both sides. Subtract one side from the other, getting a polynomial on one side and 0 on the other side. You can now use sym2poly to extract the coefficients as a vector.
Now substitute specific numeric values into the vector. double() to make the vector pure numeric. roots() to generate the potential solutions.
Now substitute the roots and the values for the coefficients back into the original (after the replacement of the derivative with a symbol) in order to validate them. Taking the square along the way potentially introduced false roots.

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