75.12.22 problem 296

Internal problem ID [16888]
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
Date solved : Tuesday, January 28, 2025 at 09:39:47 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

\begin{align*} x^{2}+y^{2}+2 x +2 y^{\prime } y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.036 (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: 5.912 (sec). Leaf size: 47

DSolve[(x^2+y[x]^2+2*x)+(2*y[x])*D[y[x],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*}