Internal problem ID [2342]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 10, The Laplace Transform and Some Elementary Applications. Exercises for 10.4.
page 689
Problem number: Problem 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-3 y^{\prime }+2 y-4 \,{\mathrm e}^{3 t}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 19
dsolve([diff(y(t),t$2)-3*diff(y(t),t)+2*y(t)=4*exp(3*t),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = -4 \,{\mathrm e}^{2 t}+2 \,{\mathrm e}^{2 t} {\mathrm e}^{t}+2 \,{\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 17
DSolve[{y''[t]-3*y'[t]+2*y[t]==4*Exp[3*t],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 2 e^t \left (e^t-1\right )^2 \\ \end{align*}