Internal problem ID [4128]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 22. Variation of Parameters
Problem number: Exercise 22.6, page 240.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+3 y^{\prime }+2 y-12 \,{\mathrm e}^{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 22
dsolve(diff(y(x),x$2)+3*diff(y(x),x)+2*y(x)=12*exp(x),y(x), singsol=all)
\[ y \relax (x ) = -c_{1} {\mathrm e}^{-2 x}+2 \,{\mathrm e}^{x}+c_{2} {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 27
DSolve[y''[x]+3*y'[x]+2*y[x]==12*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-2 x} \left (2 e^{3 x}+c_2 e^x+c_1\right ) \\ \end{align*}