52.5.11 problem 41

Internal problem ID [8334]
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
Date solved : Monday, January 27, 2025 at 03:49:09 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+y&={\mathrm e}^{-3 t} \cos \left (2 t \right ) \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 0.722 (sec). Leaf size: 28

dsolve([diff(y(t),t)+y(t)=exp(-3*t)*cos(2*t),y(0) = 0],y(t), singsol=all)
 

\[ y = \frac {{\mathrm e}^{-t}}{4}+\frac {{\mathrm e}^{-3 t} \left (-\cos \left (2 t \right )+\sin \left (2 t \right )\right )}{4} \]

✓ Solution by Mathematica

Time used: 0.121 (sec). Leaf size: 30

DSolve[{D[y[t],t]+y[t]==Exp[-3*t]*Cos[2*t],{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{4} e^{-3 t} \left (e^{2 t}+\sin (2 t)-\cos (2 t)\right ) \]