Question

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

Answer 1

\[y''-xy'''+(y''')^3=0\]

Answer 2

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

Answer 3

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, ...

Answer 4

it is as written.

Answer 5

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