90.14.15 problem 24

Internal problem ID [25243]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 3. Second Order Constant Coefficient Linear Differential Equations. Exercises at page 243
Problem number : 24
Date solved : Thursday, October 02, 2025 at 11:59:16 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-8 y^{\prime }+25 y&=104 \sin \left (3 t \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 35

ode:=diff(diff(y(t),t),t)-8*diff(y(t),t)+25*y(t) = 104*sin(3*t); 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 36

ode=D[y[t],{t,2}]-8*D[y[t],{t,1}]+25*y[t]==104*Sin[3*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \left (3+c_2 e^{4 t}\right ) \cos (3 t)+\left (2+c_1 e^{4 t}\right ) \sin (3 t) \end{align*}

✓ Sympy. Time used: 0.142 (sec). Leaf size: 34

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(25*y(t) - 104*sin(3*t) - 8*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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