Internal problem ID [12682]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 2. The Initial Value Problem. Exercises 2.3.2, page 63
Problem number: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {2 x y y^{\prime }+y^{2}=-1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve(2*x*y(x)*diff(y(x),x)+y(x)^2=-1,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\sqrt {x \left (c_{1} -x \right )}}{x} \\ y \left (x \right ) &= -\frac {\sqrt {x \left (c_{1} -x \right )}}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.471 (sec). Leaf size: 98
DSolve[2*x*y[x]*y'[x]+y[x]^2==-1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-x+e^{2 c_1}}}{\sqrt {x}} \\ y(x)\to \frac {\sqrt {-x+e^{2 c_1}}}{\sqrt {x}} \\ y(x)\to -i \\ y(x)\to i \\ y(x)\to \frac {\sqrt {-x}}{\sqrt {x}} \\ y(x)\to \frac {\sqrt {x}}{\sqrt {-x}} \\ \end{align*}