74.11.22 problem 34

Internal problem ID [16201]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number : 34
Date solved : Monday, March 31, 2025 at 02:46:39 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=25 \sin \left (2 t \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 36

ode:=diff(diff(y(t),t),t)-6*diff(y(t),t)+13*y(t) = 25*sin(2*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {\left (3 c_2 \,{\mathrm e}^{3 t}+3\right ) \sin \left (2 t \right )}{3}+{\mathrm e}^{3 t} \cos \left (2 t \right ) c_1 +\frac {4 \cos \left (2 t \right )}{3} \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 38

ode=D[y[t],{t,2}]-6*D[y[t],t]+13*y[t]==25*Sin[2*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \left (\frac {4}{3}+c_2 e^{3 t}\right ) \cos (2 t)+\left (1+c_1 e^{3 t}\right ) \sin (2 t) \]

✓ Sympy. Time used: 0.257 (sec). Leaf size: 34

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(13*y(t) - 25*sin(2*t) - 6*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (C_{1} \sin {\left (2 t \right )} + C_{2} \cos {\left (2 t \right )}\right ) e^{3 t} + \sin {\left (2 t \right )} + \frac {4 \cos {\left (2 t \right )}}{3} \]