29.6.12 problem 158

Internal problem ID [4758]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 6
Problem number : 158
Date solved : Monday, January 27, 2025 at 09:36:35 AM
CAS classification : [_linear]

\begin{align*} x y^{\prime }+x +\left (a x +2\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 35

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

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

✓ Solution by Mathematica

Time used: 0.076 (sec). Leaf size: 37

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

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