90.4.8 problem 9

Internal problem ID [25103]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 59
Problem number : 9
Date solved : Thursday, October 02, 2025 at 11:50:16 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-3 y&=25 \cos \left (4 t \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 23

ode:=diff(y(t),t)-3*y(t) = 25*cos(4*t); 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.051 (sec). Leaf size: 26

ode=D[y[t],{t,1}] -3*y[t]== 25*Cos[4*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.094 (sec). Leaf size: 22

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-3*y(t) - 25*cos(4*t) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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