Internal problem ID [3286]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 19
Problem number: 542.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _exact, _rational, _Bernoulli]
Solve \begin {gather*} \boxed {2 y y^{\prime } x +x^{2}+y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 49
dsolve(2*x*y(x)*diff(y(x),x)+x^2+y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {3}\, \sqrt {x \left (-x^{3}+3 c_{1}\right )}}{3 x} \\ y \relax (x ) = \frac {\sqrt {3}\, \sqrt {x \left (-x^{3}+3 c_{1}\right )}}{3 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.186 (sec). Leaf size: 60
DSolve[2 x y[x] y'[x]+x^2+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-x^3+3 c_1}}{\sqrt {3} \sqrt {x}} \\ y(x)\to \frac {\sqrt {-x^3+3 c_1}}{\sqrt {3} \sqrt {x}} \\ \end{align*}