40.6.1 problem 1

Internal problem ID [8633]
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 : 1
Date solved : Tuesday, September 30, 2025 at 05:40:03 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+\frac {26 y}{5}&=\frac {97 \sin \left (2 t \right )}{5} \end{align*}

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.107 (sec). Leaf size: 23

ode:=diff(y(t),t)+26/5*y(t) = 97/5*sin(2*t); 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = \frac {5 \,{\mathrm e}^{-\frac {26 t}{5}}}{4}-\frac {5 \cos \left (2 t \right )}{4}+\frac {13 \sin \left (2 t \right )}{4} \]

✓ Mathematica. Time used: 0.06 (sec). Leaf size: 37

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

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

✓ Sympy. Time used: 0.102 (sec). Leaf size: 29

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(26*y(t)/5 - 97*sin(2*t)/5 + Derivative(y(t), t),0) 
ics = {y(0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {13 \sin {\left (2 t \right )}}{4} - \frac {5 \cos {\left (2 t \right )}}{4} + \frac {5 e^{- \frac {26 t}{5}}}{4} \]