Internal problem ID [3701]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 33
Problem number: 976.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{2} \left (y^{\prime }\right )^{2}+2 y^{\prime } y x +x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.075 (sec). Leaf size: 31
dsolve(y(x)^2*diff(y(x),x)^2+2*x*y(x)*diff(y(x),x)+x^2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {-x^{2}+2 c_{1}} \\ y \relax (x ) = -\sqrt {-x^{2}+2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 39
DSolve[y[x]^2 (y'[x])^2+2 x y[x] y'[x]+x^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-x^2+2 c_1} \\ y(x)\to \sqrt {-x^2+2 c_1} \\ \end{align*}