76.2.4 problem 4

Internal problem ID [17269]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.2 (Linear equations: Method of integrating factors). Problems at page 54
Problem number : 4
Date solved : Monday, March 31, 2025 at 03:48:08 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\frac {y}{t}&=5+\cos \left (2 t \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 29

ode:=diff(y(t),t)+y(t)/t = 5+cos(2*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {10 t^{2}+4 c_1 +2 \sin \left (2 t \right ) t +\cos \left (2 t \right )}{4 t} \]

✓ Mathematica. Time used: 0.131 (sec). Leaf size: 29

ode=D[y[t],t]+(1/t)*y[t]==5+Cos[2*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {\int _1^t(\cos (2 K[1])+5) K[1]dK[1]+c_1}{t} \]

✓ Sympy. Time used: 0.345 (sec). Leaf size: 26

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-cos(2*t) + Derivative(y(t), t) - 5 + y(t)/t,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {C_{1}}{t} + \frac {5 t}{2} + \frac {\sin {\left (2 t \right )}}{2} + \frac {\cos {\left (2 t \right )}}{4 t} \]