68.18.20 problem 26

Internal problem ID [17864]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 26
Date solved : Thursday, October 02, 2025 at 02:28:59 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }&=-3 \sin \left (t \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

ode:=diff(diff(y(t),t),t)-4*diff(y(t),t) = -3*sin(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {{\mathrm e}^{4 t} c_1}{4}+\frac {3 \sin \left (t \right )}{17}-\frac {12 \cos \left (t \right )}{17}+c_2 \]

✓ Mathematica. Time used: 3.033 (sec). Leaf size: 44

ode=D[y[t],{t,2}]-4*D[y[t],t]==-3*Sin[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \int _1^te^{4 K[2]} \left (c_1+\int _1^{K[2]}-3 e^{-4 K[1]} \sin (K[1])dK[1]\right )dK[2]+c_2 \end{align*}

✓ Sympy. Time used: 0.108 (sec). Leaf size: 24

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(3*sin(t) - 4*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} + C_{2} e^{4 t} + \frac {3 \sin {\left (t \right )}}{17} - \frac {12 \cos {\left (t \right )}}{17} \]