Internal problem ID [3714]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 17
Problem number: 460.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`], _rational, _Bernoulli]
\[ \boxed {2 y y^{\prime }+y^{2}=-x^{2}-2 x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve(2*y(x)*diff(y(x),x)+2*x+x^2+y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \sqrt {c_{1} {\mathrm e}^{-x}-x^{2}} y \left (x \right ) = -\sqrt {c_{1} {\mathrm e}^{-x}-x^{2}} \end{align*}
✓ Solution by Mathematica
Time used: 6.093 (sec). Leaf size: 47
DSolve[2 y[x] y'[x]+2 x+x^2+y[x]^2==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*}