Internal problem ID [2845]
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`]]
\[ \boxed {y^{\prime }+y=5 \,{\mathrm e}^{t} \sin \left (t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 3.125 (sec). Leaf size: 23
dsolve([diff(y(t),t)+y(t)=5*exp(t)*sin(t),y(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{t} \left (2 \sin \left (t \right )-\cos \left (t \right )\right )+2 \,{\mathrm e}^{-t} \]
✓ Solution by Mathematica
Time used: 0.073 (sec). Leaf size: 27
DSolve[{y'[t]+y[t]==5*Exp[t]*Sin[t],{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to 2 e^{-t}+2 e^t \sin (t)-e^t \cos (t) \]