Internal problem ID [2344]
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 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-y-12 \,{\mathrm e}^{2 t}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.017 (sec). Leaf size: 21
dsolve([diff(y(t),t$2)-y(t)=12*exp(2*t),y(0) = 1, D(y)(0) = 1],y(t), singsol=all)
\[ y \relax (t ) = 2 \,{\mathrm e}^{-t}-5 \,{\mathrm e}^{t}+4 \,{\mathrm e}^{2 t} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 25
DSolve[{y''[t]-y[t]==12*Exp[2*t],{y[0]==1,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 2 e^{-t}-5 e^t+4 e^{2 t} \\ \end{align*}