Internal problem ID [3757]
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]
\[ \boxed {y y^{\prime } x +y^{2}=-1} \]
✓ 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 \left (x \right ) = \frac {\sqrt {-x^{2}+c_{1}}}{x} y \left (x \right ) = -\frac {\sqrt {-x^{2}+c_{1}}}{x} \end{align*}
✓ Solution by Mathematica
Time used: 0.347 (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^2}}{x} \end{align*}