Solving a Nonlinear Differential Equation with Multiple Methods

[abrowaqas]

Homework Statement

Solve the follwing differential equation
2y'-(x/y)+x^3 cosy = 0 solve?

Homework Equations

Linear Differential equation: y'+py=q
exact differential equation: Mdx+Ndy=0

The Attempt at a Solution

both of the methods i have applied ... but didnt work
later i tried it as Bernoulli Differential equation in x... but variables are not coming in

x' + px = q form...


kindly help me or give me hint to solve the above differential equation.

 

[SteamKing]

This is a non-linear ODE because of cos y. Standard linear ODE solution techniques won't work.

 

[abrowaqas]

Give me some hint ... I have also tried Cauchy and legendre methods as well ... But no one works here