Internal problem ID [3003]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 9
Problem number: 255.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}+x \left (2+x \right ) y-x \left (1-{\mathrm e}^{-2 x}\right )+2=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(x^2*diff(y(x),x)+x*(2+x)*y(x) = x*(1-exp(-2*x))-2,y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{-x} c_{1}}{x^{2}}+\frac {{\mathrm e}^{-2 x} x +{\mathrm e}^{-2 x}+x -3}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.136 (sec). Leaf size: 31
DSolve[x^2 y'[x]+x(2+x)y[x]==x(1-Exp[-2 x])-2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{-2 x} \left (x+e^x \left (e^x (x-3)+c_1\right )+1\right )}{x^2} \\ \end{align*}