Internal problem ID [3249]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 18
Problem number: 505.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y y^{\prime } x +1+y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve(x*y(x)*diff(y(x),x)+1+y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {-x^{2}+c_{1}}}{x} \\ y \relax (x ) = -\frac {\sqrt {-x^{2}+c_{1}}}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.322 (sec). Leaf size: 96
DSolve[x y[x] y'[x]+1+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-x^2+e^{2 c_1}}}{x} \\ y(x)\to \frac {\sqrt {-x^2+e^{2 c_1}}}{x} \\ y(x)\to -i \\ y(x)\to i \\ y(x)\to \frac {x}{\sqrt {-x^2}} \\ y(x)\to \frac {\sqrt {-x}}{\sqrt {x}} \\ \end{align*}