Question

(x^2 )dy/dx- xy = 1 - cos(y/x)
find the general solution for the above equation .

Answer 1

Final Answer : y= 2xcot-1((cx^2+1)/2x^2)

This is First order Non Linear Ordinary Differential Equation.

Steps :
1) Use Trigonometric Identity to convert RHS into sin function.
2) Use substitution y = vx where v is some function.
3) Solve, ODE.