Internal problem ID [5913]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 7 THE LAPLACE TRANSFORM. 7.2.2 TRANSFORMS OF DERIVATIVES
Page 289
Problem number: 41.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }+y-{\mathrm e}^{-3 t} \cos \left (2 t \right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 28
dsolve([diff(y(t),t)+y(t)=exp(-3*t)*cos(2*t),y(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = -\frac {\left (-1+\left (\cos \left (2 t \right )-\sin \left (2 t \right )\right ) {\mathrm e}^{-2 t}\right ) {\mathrm e}^{-t}}{4} \]
✓ Solution by Mathematica
Time used: 0.107 (sec). Leaf size: 30
DSolve[{y'[t]+y[t]==Exp[-3*t]*Cos[2*t],{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{4} e^{-3 t} \left (e^{2 t}+\sin (2 t)-\cos (2 t)\right ) \\ \end{align*}