52.5.3 problem 33

Internal problem ID [8326]
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 : 33
Date solved : Monday, January 27, 2025 at 03:49:04 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+6 y&={\mathrm e}^{4 t} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.665 (sec). Leaf size: 16

dsolve([diff(y(t),t)+6*y(t)=exp(4*t),y(0) = 2],y(t), singsol=all)
 

\[ y = \frac {\left ({\mathrm e}^{10 t}+19\right ) {\mathrm e}^{-6 t}}{10} \]

✓ Solution by Mathematica

Time used: 0.050 (sec). Leaf size: 21

DSolve[{D[y[t],t]+6*y[t]==Exp[4*t],{y[0]==2}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{10} e^{-6 t} \left (e^{10 t}+19\right ) \]