Internal problem ID [6666]
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`]]
\[ \boxed {y^{\prime }+y={\mathrm e}^{-3 t} \cos \left (2 t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 2.0 (sec). Leaf size: 28
dsolve([diff(y(t),t)+y(t)=exp(-3*t)*cos(2*t),y(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {{\mathrm e}^{-t}}{4}+\frac {{\mathrm e}^{-3 t} \left (-\cos \left (2 t \right )+\sin \left (2 t \right )\right )}{4} \]
✓ Solution by Mathematica
Time used: 0.124 (sec). Leaf size: 30
DSolve[{y'[t]+y[t]==Exp[-3*t]*Cos[2*t],{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{4} e^{-3 t} \left (e^{2 t}+\sin (2 t)-\cos (2 t)\right ) \]