Internal problem ID [8027]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 449.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}+2 y x y^{\prime }+y^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve((-a^2+x^2)*diff(y(x),x)^2+2*x*y(x)*diff(y(x),x)+y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {c_{1}}{-x +a} \\ y \left (x \right ) = \frac {c_{1}}{a +x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.05 (sec). Leaf size: 32
DSolve[y[x]^2 + 2*x*y[x]*y'[x] + (-a^2 + x^2)*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1}{a-x} \\ y(x)\to \frac {c_1}{a+x} \\ y(x)\to 0 \\ \end{align*}