Internal problem ID [8568]
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]
\[ \boxed {x y^{\prime } y+y^{2}=-x^{2}} \]
✓ Solution by Maple
Time used: 0.016 (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 \left (x \right ) &= -\frac {\sqrt {-2 x^{4}+4 c_{1}}}{2 x} \\ y \left (x \right ) &= \frac {\sqrt {-2 x^{4}+4 c_{1}}}{2 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.215 (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*}