Internal problem ID [7822]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 242.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {2 x y y^{\prime }+2 y^{2}+1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 39
dsolve(2*x*y(x)*diff(y(x),x)+2*y(x)^2+1=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {-2 x^{2}+4 c_{1}}}{2 x} \\ y \relax (x ) = \frac {\sqrt {-2 x^{2}+4 c_{1}}}{2 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.337 (sec). Leaf size: 128
DSolve[2*x*y[x]*y'[x]+2*y[x]^2+1==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-x^2+e^{4 c_1}}}{\sqrt {2} x} \\ y(x)\to \frac {\sqrt {-x^2+e^{4 c_1}}}{\sqrt {2} x} \\ y(x)\to -\frac {i}{\sqrt {2}} \\ y(x)\to \frac {i}{\sqrt {2}} \\ y(x)\to \frac {x}{\sqrt {2} \sqrt {-x^2}} \\ y(x)\to \frac {\sqrt {-x}}{\sqrt {2} \sqrt {x}} \\ \end{align*}