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

Answer 1

[Walter Roberson]

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.

[loyal]

However, this code in the matlab22 version before the version, there is no way to achieve, how to solve? Thanks again!

[loyal]

And Is sol two solutions or a sum?by the way? Thank u

[loyal]

Thank you so much

[Walter Roberson]

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]

Sorry, I mean versions younger than 2022 will not work。It solved Thank you so much！ Have a good day