Internal problem ID [2906]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 6
Problem number: 158.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime } x +x +\left (a x +2\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 36
dsolve(x*diff(y(x),x)+x+(a*x+2)*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {1}{a}+\frac {2}{a^{2} x}-\frac {2}{a^{3} x^{2}}+\frac {{\mathrm e}^{-a x} c_{1}}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.06 (sec). Leaf size: 34
DSolve[x y'[x]+x+(2+a x)y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\frac {a x (2-a x)-2}{a^3}+c_1 e^{-a x}}{x^2} \\ \end{align*}