Internal problem ID [3265]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 19
Problem number: 521.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {x \left (y+2\right ) y^{\prime }+a x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 37
dsolve(x*(2+y(x))*diff(y(x),x)+a*x = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -2-\sqrt {-2 c_{1} a -2 a x +4} \\ y \relax (x ) = -2+\sqrt {-2 c_{1} a -2 a x +4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.147 (sec). Leaf size: 50
DSolve[x(2+y[x])y'[x]+a x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -2-\sqrt {2} \sqrt {-a x+2+c_1} \\ y(x)\to -2+\sqrt {2} \sqrt {-a x+2+c_1} \\ \end{align*}