Internal problem ID [8680]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1100.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime } x +2 y^{\prime }-y x -{\mathrm e}^{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 23
dsolve(x*diff(diff(y(x),x),x)+2*diff(y(x),x)-x*y(x)-exp(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\sinh \relax (x ) c_{2}}{x}+\frac {\cosh \relax (x ) c_{1}}{x}+\frac {{\mathrm e}^{x}}{2} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 37
DSolve[-E^x - x*y[x] + 2*y'[x] + x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{-x} \left (e^{2 x} (2 x-1+2 c_2)+4 c_1\right )}{4 x} \\ \end{align*}