Solving Lagrange equation.

Question

Please help me solving the equation.

I found one of its solutions: $c_1=(xz)/y$

But another one is given as $c_2=(x^3/y)+x$ in the text book. But I cont find. Thank you.

Answer 1

Hints:

• Rewrite the equation in terms of $\dfrac{dy}{dx}$
• Make the substitution $y = v~x$
• You end up with a first order equation, use Integrating Factor