Internal problem ID [3623]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 30
Problem number: 895.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x^{2} \left (y^{\prime }\right )^{2}+y^{2}-y^{4}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.391 (sec). Leaf size: 66
dsolve(x^2*diff(y(x),x)^2+y(x)^2-y(x)^4 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -1 \\ y \relax (x ) = 1 \\ y \relax (x ) = 0 \\ y \relax (x ) = \frac {\sqrt {\tan ^{2}\left (-\ln \relax (x )+c_{1}\right )+1}}{\tan \left (-\ln \relax (x )+c_{1}\right )} \\ y \relax (x ) = -\frac {\sqrt {\tan ^{2}\left (-\ln \relax (x )+c_{1}\right )+1}}{\tan \left (-\ln \relax (x )+c_{1}\right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.304 (sec). Leaf size: 88
DSolve[x^2 (y'[x])^2+y[x]^2-y[x]^4==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {\sec ^2(-\log (x)+c_1)} \\ y(x)\to \sqrt {\sec ^2(-\log (x)+c_1)} \\ y(x)\to -\sqrt {\sec ^2(\log (x)+c_1)} \\ y(x)\to \sqrt {\sec ^2(\log (x)+c_1)} \\ y(x)\to -1 \\ y(x)\to 0 \\ y(x)\to 1 \\ \end{align*}