Internal problem ID [3322]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 21
Problem number: 580.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {2 \left (x +1\right ) x y y^{\prime }-1-y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 42
dsolve(2*(1+x)*x*y(x)*diff(y(x),x) = 1+y(x)^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {\left (x +1\right ) \left (c_{1} x -1\right )}}{x +1} \\ y \relax (x ) = -\frac {\sqrt {\left (x +1\right ) \left (c_{1} x -1\right )}}{x +1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.682 (sec). Leaf size: 114
DSolve[2(1+x)x y[x] y'[x]==1+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-1+\left (-1+e^{2 c_1}\right ) x}}{\sqrt {x+1}} \\ y(x)\to \frac {\sqrt {-1+\left (-1+e^{2 c_1}\right ) x}}{\sqrt {x+1}} \\ y(x)\to -i \\ y(x)\to i \\ y(x)\to \frac {\sqrt {x+1}}{\sqrt {-x-1}} \\ y(x)\to \frac {\sqrt {-x-1}}{\sqrt {x+1}} \\ \end{align*}