Internal problem ID [2498]
Book: Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section: Exercises, page 14
Problem number: 1(f).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (x +1\right ) y^{\prime }-x^{2} y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 24
dsolve((x+1)*diff(y(x),x)-x^2*y(x)^2=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {2}{x^{2}+2 \ln \left (x +1\right )-2 c_{1}-2 x} \]
✓ Solution by Mathematica
Time used: 0.16 (sec). Leaf size: 31
DSolve[(x+1)*y'[x]-x^2*y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {2}{(x-2) x+2 \log (x+1)-3+2 c_1} \\ y(x)\to 0 \\ \end{align*}