Internal problem ID [8578]
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]
\[ \boxed {2 y^{\prime } x y+2 y^{2}=-1} \]
✓ Solution by Maple
Time used: 0.016 (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 \left (x \right ) = -\frac {\sqrt {-2 x^{2}+4 c_{1}}}{2 x} y \left (x \right ) = \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^2}}{\sqrt {2} x} \end{align*}