6.12 problem 158

Internal problem ID [3414]

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]

\[ \boxed {x y^{\prime }+\left (a x +2\right ) y=-x} \]

Solution by Maple

Time used: 0.016 (sec). Leaf size: 35

dsolve(x*diff(y(x),x)+x+(a*x+2)*y(x) = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {{\mathrm e}^{-a x} c_{1} a^{3}-x^{2} a^{2}+2 a x -2}{a^{3} x^{2}} \]

Solution by Mathematica

Time used: 0.06 (sec). Leaf size: 37

DSolve[x y'[x]+x+(2+a x)y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {-\frac {a^2 x^2-2 a x+2}{a^3}+c_1 e^{-a x}}{x^2} \]