Internal problem ID [2345]
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 16.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y-10 \,{\mathrm e}^{-t}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 4, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 21
dsolve([diff(y(t),t$2)+4*y(t)=10*exp(-t),y(0) = 4, D(y)(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = \sin \left (2 t \right )+2 \cos \left (2 t \right )+2 \,{\mathrm e}^{-t} \]
✓ Solution by Mathematica
Time used: 0.04 (sec). Leaf size: 23
DSolve[{y''[t]+4*y[t]==10*Exp[-t],{y[0]==4,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 2 e^{-t}+\sin (2 t)+2 \cos (2 t) \\ \end{align*}