Internal problem ID [242]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number: 47.
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-4 \,{\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)=4*exp(x),y(x), singsol=all)
\[ y \relax (x ) = -{\mathrm e}^{-2 x} c_{1}+\frac {2 \,{\mathrm e}^{x}}{3}+{\mathrm e}^{-x} c_{2} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 29
DSolve[y''[x]+3*y'[x]+2*y[x]==4*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 e^x}{3}+c_1 e^{-2 x}+c_2 e^{-x} \\ \end{align*}