Internal problem ID [685]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 3, Second order linear equations, section 3.6, Variation of Parameters. page
190
Problem number: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 y^{\prime }+y-3 \,{\mathrm e}^{-t}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 27
dsolve(diff(y(t),t$2)+2*diff(y(t),t)+y(t) = 3*exp(-t),y(t), singsol=all)
\[ y \relax (t ) = c_{2} {\mathrm e}^{-t}+t \,{\mathrm e}^{-t} c_{1}+\frac {3 t^{2} {\mathrm e}^{-t}}{2} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 29
DSolve[y''[t]+2*y'[t]+y[t] == 3*Exp[-t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{2} e^{-t} \left (3 t^2+2 c_2 t+2 c_1\right ) \\ \end{align*}