Internal problem ID [227]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number: 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 y^{\prime }-3 y-1-{\mathrm e}^{x} x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 30
dsolve(diff(y(x),x$2)+2*diff(y(x),x)-3*y(x)=1+x*exp(x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-3 x} c_{2}+{\mathrm e}^{x} c_{1}-\frac {1}{3}+\frac {\left (24 x^{2}-12 x +3\right ) {\mathrm e}^{x}}{192} \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 38
DSolve[y''[x]+2*y'[x]-3*y[x]==1+x*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{64} e^x \left (8 x^2-4 x+1+64 c_2\right )+c_1 e^{-3 x}-\frac {1}{3} \\ \end{align*}