46.6.1 problem 1

Internal problem ID [7347]
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 : Wednesday, March 05, 2025 at 04:23:48 AM
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: 0.280 (sec). Leaf size: 23

ode:=diff(y(t),t)+26/5*y(t) = 97/5*sin(2*t); 
ic:=y(0) = 0; 
dsolve([ode,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: 0.09 (sec). Leaf size: 31

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]
 

\[ y(t)\to \frac {1}{4} \left (5 e^{-26 t/5}+13 \sin (2 t)-5 \cos (2 t)\right ) \]

✓ Sympy. Time used: 0.195 (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)
 

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