29.9.15 problem 255

Internal problem ID [4855]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 9
Problem number : 255
Date solved : Monday, January 27, 2025 at 09:42:49 AM
CAS classification : [_linear]

\begin{align*} x^{2} y^{\prime }+x \left (x +2\right ) y&=x \left (1-{\mathrm e}^{-2 x}\right )-2 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 27

dsolve(x^2*diff(y(x),x)+x*(2+x)*y(x) = x*(1-exp(-2*x))-2,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.177 (sec). Leaf size: 32

DSolve[x^2*D[y[x],x]+x*(2+x)*y[x]==x*(1-Exp[-2*x])-2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{-2 x} \left (e^{2 x} (x-3)+x+c_1 e^x+1\right )}{x^2} \]