Internal problem ID [3692]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 33
Problem number: 967.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x y \left (y^{\prime }\right )^{2}+\left (3 x^{2}-2 y^{2}\right ) y^{\prime }-6 y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 35
dsolve(x*y(x)*diff(y(x),x)^2+(3*x^2-2*y(x)^2)*diff(y(x),x)-6*x*y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = c_{1} x^{2} \\ y \relax (x ) = \sqrt {-3 x^{2}+c_{1}} \\ y \relax (x ) = -\sqrt {-3 x^{2}+c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.129 (sec). Leaf size: 54
DSolve[x y[x] (y'[x])^2+(3 x^2-2 y[x]^2)y'[x]-6 x y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x^2 \\ y(x)\to -\sqrt {-3 x^2+2 c_1} \\ y(x)\to \sqrt {-3 x^2+2 c_1} \\ y(x)\to 0 \\ \end{align*}