40.6.2 problem 2

Internal problem ID [8634]
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 : 2
Date solved : Tuesday, September 30, 2025 at 05:40:03 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }+2 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&={\frac {3}{2}} \\ \end{align*}

✓ Maple. Time used: 0.097 (sec). Leaf size: 10

ode:=diff(y(t),t)+2*y(t) = 0; 
ic:=[y(0) = 3/2]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = \frac {3 \,{\mathrm e}^{-2 t}}{2} \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 44

ode=D[y[t],t]+52/10*y[t]==194/10*Sin[2*t]; 
ic={y[0]==15/10}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {1}{2} e^{-26 t/5} \left (2 \int _0^t\frac {97}{5} e^{\frac {26 K[1]}{5}} \sin (2 K[1])dK[1]+3\right ) \end{align*}

✓ Sympy. Time used: 0.062 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(2*y(t) + Derivative(y(t), t),0) 
ics = {y(0): 3/2} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {3 e^{- 2 t}}{2} \]