Internal problem ID [2853]
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]]
\[ \boxed {y^{\prime \prime }-y=12 \,{\mathrm e}^{2 t}} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 2.953 (sec). Leaf size: 19
dsolve([diff(y(t),t$2)-y(t)=12*exp(2*t),y(0) = 1, D(y)(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = -3 \cosh \left (t \right )-7 \sinh \left (t \right )+4 \,{\mathrm e}^{2 t} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 25
DSolve[{y''[t]-y[t]==12*Exp[2*t],{y[0]==1,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to 2 e^{-t}-5 e^t+4 e^{2 t} \]