Internal problem ID [3792]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 19
Problem number: 540.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {2 y y^{\prime } x +y^{2}=-a} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 36
dsolve(2*x*y(x)*diff(y(x),x)+a+y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {\sqrt {\left (-a x +c_{1} \right ) x}}{x} y \left (x \right ) = -\frac {\sqrt {\left (-a x +c_{1} \right ) x}}{x} \end{align*}
✓ Solution by Mathematica
Time used: 0.358 (sec). Leaf size: 115
DSolve[2 x y[x] y'[x]+a+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-a x+e^{2 c_1}}}{\sqrt {x}} y(x)\to \frac {\sqrt {-a x+e^{2 c_1}}}{\sqrt {x}} y(x)\to -i \sqrt {a} y(x)\to i \sqrt {a} y(x)\to \frac {a \sqrt {x}}{\sqrt {-a x}} y(x)\to \frac {\sqrt {-a x}}{\sqrt {x}} \end{align*}