52.5.4 problem 34

Internal problem ID [8327]
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
Date solved : Monday, January 27, 2025 at 03:49:04 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-y&=2 \cos \left (5 t \right ) \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.708 (sec). Leaf size: 21

dsolve([diff(y(t),t)-y(t)=2*cos(5*t),y(0) = 0],y(t), singsol=all)
 

\[ y = \frac {{\mathrm e}^{t}}{13}-\frac {\cos \left (5 t \right )}{13}+\frac {5 \sin \left (5 t \right )}{13} \]

✓ Solution by Mathematica

Time used: 0.098 (sec). Leaf size: 25

DSolve[{D[y[t],t]-y[t]==2*Cos[5*t],{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{13} \left (e^t+5 \sin (5 t)-\cos (5 t)\right ) \]