46.6.6 problem 6

Internal problem ID [7352]
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 : 6
Date solved : Wednesday, March 05, 2025 at 04:23:53 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+5 y&=29 \cos \left (2 t \right ) \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&={\frac {16}{5}}\\ y^{\prime }\left (0\right )&={\frac {31}{5}} \end{align*}

✓ Maple. Time used: 0.267 (sec). Leaf size: 25

ode:=diff(diff(y(t),t),t)-6*diff(y(t),t)+5*y(t) = 29*cos(2*t); 
ic:=y(0) = 16/5, D(y)(0) = 31/5; 
dsolve([ode,ic],y(t),method='laplace');
 

\[ y = {\mathrm e}^{t}+\frac {\cos \left (2 t \right )}{5}-\frac {12 \sin \left (2 t \right )}{5}+2 \,{\mathrm e}^{5 t} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 32

ode=D[y[t],{t,2}]-6*D[y[t],t]+5*y[t]==29*Cos[2*t]; 
ic={y[0]==32/10,Derivative[1][y][0] ==62/10}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^t+2 e^{5 t}-\frac {12}{5} \sin (2 t)+\frac {1}{5} \cos (2 t) \]

✓ Sympy. Time used: 0.308 (sec). Leaf size: 27

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(5*y(t) - 29*cos(2*t) - 6*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 16/5, Subs(Derivative(y(t), t), t, 0): 31/5} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 2 e^{5 t} + e^{t} - \frac {12 \sin {\left (2 t \right )}}{5} + \frac {\cos {\left (2 t \right )}}{5} \]