Internal problem ID [15158]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 12. Miscellaneous problems. Exercises page 93
Problem number: 296.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`], _rational, _Bernoulli]
\[ \boxed {y^{2}+2 y y^{\prime }=-x^{2}-2 x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 37
dsolve((x^2+y(x)^2+2*x)+(2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y &= \sqrt {c_{1} {\mathrm e}^{-x}-x^{2}} \\ y &= -\sqrt {c_{1} {\mathrm e}^{-x}-x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 5.559 (sec). Leaf size: 47
DSolve[(x^2+y[x]^2+2*x)+(2*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-x^2+c_1 e^{-x}} \\ y(x)\to \sqrt {-x^2+c_1 e^{-x}} \\ \end{align*}