68.11.21 problem 33

Internal problem ID [17558]
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 : 33
Date solved : Thursday, October 02, 2025 at 02:25:24 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }&=52 \sin \left (3 t \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 25

ode:=diff(diff(y(t),t),t)-2*diff(y(t),t) = 52*sin(3*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {{\mathrm e}^{2 t} c_1}{2}-4 \sin \left (3 t \right )+\frac {8 \cos \left (3 t \right )}{3}+c_2 \]

✓ Mathematica. Time used: 3.169 (sec). Leaf size: 46

ode=D[y[t],{t,2}]-2*D[y[t],t]==52*Sin[3*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \int _1^te^{2 K[2]} \left (c_1+\int _1^{K[2]}52 e^{-2 K[1]} \sin (3 K[1])dK[1]\right )dK[2]+c_2 \end{align*}

✓ Sympy. Time used: 0.118 (sec). Leaf size: 26

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-52*sin(3*t) - 2*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} + C_{2} e^{2 t} - 4 \sin {\left (3 t \right )} + \frac {8 \cos {\left (3 t \right )}}{3} \]