Internal problem ID [2336]
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 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }+y-5 \,{\mathrm e}^{t} \sin \relax (t )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 23
dsolve([diff(y(t),t)+y(t)=5*exp(t)*sin(t),y(0) = 1],y(t), singsol=all)
\[ y \relax (t ) = 2 \,{\mathrm e}^{-t}+\left (-\cos \relax (t )+2 \sin \relax (t )\right ) {\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.077 (sec). Leaf size: 25
DSolve[{y'[t]+y[t]==5*Exp[t]*Sin[t],{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 2 e^{-t}-e^t (\cos (t)-2 \sin (t)) \\ \end{align*}