Internal problem ID [5906]
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: 34.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-y-2 \cos \left (5 t \right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve([diff(y(t),t)-y(t)=2*cos(5*t),y(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = -\frac {\cos \left (5 t \right )}{13}+\frac {5 \sin \left (5 t \right )}{13}+\frac {{\mathrm e}^{t}}{13} \]
✓ Solution by Mathematica
Time used: 0.13 (sec). Leaf size: 25
DSolve[{y'[t]-y[t]==2*Cos[5*t],{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{13} \left (e^t+5 \sin (5 t)-\cos (5 t)\right ) \\ \end{align*}