Internal problem ID [3493]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 26
Problem number: 760.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-x^{2} y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x)^2 = x^2*y(x)^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = {\mathrm e}^{\frac {x^{2}}{2}} c_{1} \\ y \relax (x ) = c_{1} {\mathrm e}^{-\frac {x^{2}}{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.045 (sec). Leaf size: 38
DSolve[(y'[x])^2==x^2 y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-\frac {x^2}{2}} \\ y(x)\to c_1 e^{\frac {x^2}{2}} \\ y(x)\to 0 \\ \end{align*}