How to solve this non-linear differential equation: y''-x*y'''+(y''')^3=0
@Mathematics @Calculus1

Question

anonymous · Answer

$$y''-xy'''+(y''')^3=0$$

turingtest · Answer

That is NOT calculus 1.
Though I guess there is no differential equations section...

jamesj · Answer

If the equation is with (y'')^3, then the equation is
xu' - u = u^3,
where u = y''

This is a Bernoulli equation and very doable.

But if the equation is as written, ...

anonymous · Answer

it is as written.

jamesj · Answer

Writing as before u = y'', use an Ansatz of 
u = Ax + B
u' = A

Then as u - xu' + (u')^3 = 0,
Ax + B - Ax + A^3 = 0 => B = -A^3

i.e., u = Ax - A^3

Now integrate twice to find y