Internal problem ID [2343]
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 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y^{\prime }-30 \,{\mathrm e}^{-3 t}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve([diff(y(t),t$2)-2*diff(y(t),t)=30*exp(-3*t),y(0) = 1, D(y)(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = \left (3 \,{\mathrm e}^{5 t}-4 \,{\mathrm e}^{3 t}+2\right ) {\mathrm e}^{-3 t} \]
✓ Solution by Mathematica
Time used: 0.081 (sec). Leaf size: 21
DSolve[{y''[t]-2*y'[t]==30*Exp[-3*t],{y[0]==1,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 2 e^{-3 t}+3 e^{2 t}-4 \\ \end{align*}