Internal problem ID [3214]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 17
Problem number: 468.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational, [_1st_order, _with_symmetry_[F(x),G(x)]], [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {2 \left (x +y\right ) y^{\prime }+x^{2}+2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 51
dsolve(2*(x+y(x))*diff(y(x),x)+x^2+2*y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -x -\frac {\sqrt {-3 x^{3}+9 x^{2}-9 c_{1}}}{3} \\ y \relax (x ) = -x +\frac {\sqrt {-3 x^{3}+9 x^{2}-9 c_{1}}}{3} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.148 (sec). Leaf size: 53
DSolve[2(x+y[x])y'[x]+x^2+2 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x-\sqrt {-\frac {x^3}{3}+x^2+c_1} \\ y(x)\to -x+\sqrt {-\frac {x^3}{3}+x^2+c_1} \\ \end{align*}