Internal problem ID [7812]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 232.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {x y y^{\prime }+y^{2}+x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
dsolve(x*y(x)*diff(y(x),x)+y(x)^2+x^2=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {-2 x^{4}+4 c_{1}}}{2 x} \\ y \relax (x ) = \frac {\sqrt {-2 x^{4}+4 c_{1}}}{2 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.218 (sec). Leaf size: 46
DSolve[x*y[x]*y'[x]+y[x]^2+x^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-\frac {x^4}{2}+c_1}}{x} \\ y(x)\to \frac {\sqrt {-\frac {x^4}{2}+c_1}}{x} \\ \end{align*}