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 : Wednesday, March 05, 2025 at 05:35:14 AM
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*}

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

ode:=diff(y(t),t)+6*y(t) = exp(4*t); 
ic:=y(0) = 2; 
dsolve([ode,ic],y(t),method='laplace');
 

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

✓ Mathematica. Time used: 0.05 (sec). Leaf size: 21

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

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

✓ Sympy. Time used: 0.162 (sec). Leaf size: 17

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(6*y(t) - exp(4*t) + Derivative(y(t), t),0) 
ics = {y(0): 2} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {e^{4 t}}{10} + \frac {19 e^{- 6 t}}{10} \]