Internal problem ID [2935]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 7
Problem number: 187.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } x -y \left (1+y^{2}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 30
dsolve(x*diff(y(x),x) = y(x)*(1+y(x)^2),y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {x}{\sqrt {-x^{2}+c_{1}}} \\ y \relax (x ) = -\frac {x}{\sqrt {-x^{2}+c_{1}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.544 (sec). Leaf size: 110
DSolve[x y'[x]==y[x](1+y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {i e^{c_1} x}{\sqrt {-1+e^{2 c_1} x^2}} \\ y(x)\to \frac {i e^{c_1} x}{\sqrt {-1+e^{2 c_1} x^2}} \\ y(x)\to 0 \\ y(x)\to -i \\ y(x)\to i \\ y(x)\to -\frac {i x}{\sqrt {x^2}} \\ y(x)\to \frac {i x}{\sqrt {x^2}} \\ \end{align*}