Internal problem ID [10282]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VIII, Linear differential equations of the second order. Article 53. Change of
dependent variable. Page 125
Problem number: Ex 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }+2 y^{\prime }-y x -2 \,{\mathrm e}^{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve(x*diff(y(x),x$2)+2*diff(y(x),x)-x*y(x)=2*exp(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {\sinh \relax (x ) c_{2}}{x}+\frac {\cosh \relax (x ) c_{1}}{x}+{\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 35
DSolve[x*y''[x]+2*y'[x]-x*y[x]==2*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{-x} \left (e^{2 x} (2 x-1+c_2)+2 c_1\right )}{2 x} \\ \end{align*}