# Solving Lagrange 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.

• Rewrite the equation in terms of $\dfrac{dy}{dx}$
• Make the substitution $y = v~x$
• Where you see a $y$ substitute $vx$. Where you see a $dy/dx$, substitute $v + xv'$. – Amzoti Nov 2 '13 at 18:24
• I get $dy/dx=3y/x+y^2/x^3$ and then? – Nrsnr Nov 2 '13 at 18:24
• Okay now I get $x^2v'=2xv+v^2$ – Nrsnr Nov 2 '13 at 18:27
• Now do the substitutions I listed above and you have a DEQ in terms of $dv/dx$, solve that and then substitute back. – Amzoti Nov 2 '13 at 18:27