How to use matlab to solve the expression of w with respect to x?

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loyal
loyal 2023-5-16
评论： loyal 2023-5-16

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Walter Roberson
Walter Roberson 2023-5-16
Ran in:
syms w(x)
syms c real
dw = diff(w); d2w = diff(dw);
eqn = d2w/(1+dw^2)^(3/2) == c*x
eqn(x) = 
sol = dsolve(eqn)
sol = 
The integrals are possibly not expressable in closed form solutions.
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Walter Roberson
Walter Roberson 2023-5-16
R2022a:
>> syms w(x)
syms c real
dw = diff(w); d2w = diff(dw);
eqn = d2w/(1+dw^2)^(3/2) == c*x
sol = dsolve(eqn)
eqn(x) =
diff(w(x), x, x)/(diff(w(x), x)^2 + 1)^(3/2) == c*x
sol =
C2 + int(((-(c*x^2 + 2*C1 - 2)*(c*x^2 + 2*C1 + 2))^(1/2)*(c*x^2 + 2*C1))/(4*C1^2 + 4*C1*c*x^2 + c^2*x^4 - 4), x, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)
C3 + int((c*x^2 + 2*C1)/(- 4*C1^2 - 4*C1*c*x^2 - c^2*x^4 + 4)^(1/2), x, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)
So I do not know what you are seeing that leads you to think that the R2022* versions are unable to solve this the same way as the current version.
Those are two solutions. not a sum. You can access sol(1) and sol(2)
loyal
loyal 2023-5-16
Sorry, I mean versions younger than 2022 will not work。It solved Thank you so much！ Have a good day

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