Internal problem ID [2340]
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 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-y^{\prime }-12 y-36=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 12] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 12
dsolve([diff(y(t),t$2)-diff(y(t),t)-12*y(t)=36,y(0) = 0, D(y)(0) = 12],y(t), singsol=all)
\[ y \relax (t ) = 3 \,{\mathrm e}^{4 t}-3 \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 14
DSolve[{y''[t]-y'[t]-12*y[t]==36,{y[0]==0,y'[0]==12}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 3 \left (e^{4 t}-1\right ) \\ \end{align*}