Internal problem ID [8011]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 431.
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^{4}+y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.395 (sec). Leaf size: 66
dsolve(x^2*diff(y(x),x)^2-y(x)^4+y(x)^2 = 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: 1.472 (sec). Leaf size: 88
DSolve[y[x]^2 - y[x]^4 + x^2*y'[x]^2==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*}