Internal problem ID [251]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number: 56.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-4 y-{\mathrm e}^{x} x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)-4*y(x)=x*exp(x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-2 x} c_{2}+c_{1} {\mathrm e}^{2 x}-\frac {\left (3 x +2\right ) {\mathrm e}^{x}}{9} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 34
DSolve[y''[x]-4*y[x]==x*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{9} e^x (3 x+2)+c_1 e^{2 x}+c_2 e^{-2 x} \\ \end{align*}