Internal problem ID [3206]
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]
Solve \begin {gather*} \boxed {2 y y^{\prime }+2 x +x^{2}+y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (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 \relax (x ) = \sqrt {{\mathrm e}^{-x} c_{1}-x^{2}} \\ y \relax (x ) = -\sqrt {{\mathrm e}^{-x} c_{1}-x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.455 (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*}