76.2.11 problem 11

Internal problem ID [17276]
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 : 11
Date solved : Monday, March 31, 2025 at 03:48:25 PM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 21

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

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

✓ Mathematica. Time used: 0.058 (sec). Leaf size: 32

ode=D[y[t],t]+y[t]==5*Sin[2*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{-t} \left (\int _1^t5 e^{K[1]} \sin (2 K[1])dK[1]+c_1\right ) \]

✓ Sympy. Time used: 0.134 (sec). Leaf size: 19

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

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