Internal problem ID [2631]
Book: An introduction to the solution and applications of differential equations, J.W. Searl,
1966
Section: Chapter 4, Ex. 4.2
Problem number: 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x^{2} \left (1+y^{2}\right ) y^{\prime }+y^{2} \left (x^{2}+1\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 94
dsolve(x^2*(1+y(x)^2)*diff(y(x),x)+y(x)^2*(x^2+1)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {-c_{1} x -x^{2}+1+\sqrt {x^{4}+2 x^{3} c_{1}+x^{2} c_{1}^{2}+2 x^{2}-2 c_{1} x +1}}{2 x} \\ y \relax (x ) = -\frac {c_{1} x +x^{2}+\sqrt {x^{4}+2 x^{3} c_{1}+x^{2} c_{1}^{2}+2 x^{2}-2 c_{1} x +1}-1}{2 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.158 (sec). Leaf size: 95
DSolve[x^2*(1+y[x]^2)*y'[x]+y[x]^2*(x^2+1)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x^2+\sqrt {4 x^2+\left (-x^2+c_1 x+1\right ){}^2}-c_1 x-1}{2 x} \\ y(x)\to \frac {-x^2+\sqrt {4 x^2+\left (-x^2+c_1 x+1\right ){}^2}+c_1 x+1}{2 x} \\ y(x)\to 0 \\ \end{align*}