40.6.13 problem 13

Internal problem ID [8645]
Book : ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG, EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section : Chapter 6. Laplace Transforms. Problem set 6.2, page 216
Problem number : 13
Date solved : Tuesday, September 30, 2025 at 05:40:09 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }-6 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (-1\right )&=4 \\ \end{align*}

✓ Maple. Time used: 0.082 (sec). Leaf size: 12

ode:=diff(y(t),t)-6*y(t) = 0; 
ic:=[y(-1) = 4]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = 4 \,{\mathrm e}^{6 t +6} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 14

ode=D[y[t],t]-6*y[t]==0; 
ic={y[-1]==4}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to 4 e^{6 t+6} \end{align*}

✓ Sympy. Time used: 0.061 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-6*y(t) + Derivative(y(t), t),0) 
ics = {y(-1): 4} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 4 e^{6} e^{6 t} \]