Internal problem ID [2986]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 8
Problem number: 238.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {2 y^{\prime } x -y \left (1+y^{2}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 42
dsolve(2*x*diff(y(x),x) = y(x)*(1+y(x)^2),y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {\left (-x +c_{1}\right ) x}}{-x +c_{1}} \\ y \relax (x ) = -\frac {\sqrt {\left (-x +c_{1}\right ) x}}{-x +c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.518 (sec). Leaf size: 82
DSolve[2 x y'[x]==y[x](1+y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {i e^{c_1} \sqrt {x}}{\sqrt {-1+e^{2 c_1} x}} \\ y(x)\to \frac {i e^{c_1} \sqrt {x}}{\sqrt {-1+e^{2 c_1} x}} \\ y(x)\to 0 \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}