Internal problem ID [232]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number: 25.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+3 y^{\prime }+2 y-x \left ({\mathrm e}^{-x}-{\mathrm e}^{-2 x}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 45
dsolve(diff(y(x),x$2)+3*diff(y(x),x)+2*y(x)=x*(exp(-x)-exp(-2*x)),y(x), singsol=all)
\[ y \relax (x ) = \left (-{\mathrm e}^{-x} c_{1}+\frac {x^{2}}{2}-x +\frac {{\mathrm e}^{-x} x^{2}}{2}+x \,{\mathrm e}^{-x}+{\mathrm e}^{-x}+c_{2}\right ) {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.035 (sec). Leaf size: 41
DSolve[y''[x]+3*y'[x]+2*y[x]==x*(Exp[-x]-Exp[-2*x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} e^{-2 x} \left (x^2+e^x \left (x^2-2 x+2+2 c_2\right )+2 (x+1+c_1)\right ) \\ \end{align*}