10.1.11 problem 11

Internal problem ID [1108]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 11
Date solved : Tuesday, March 04, 2025 at 12:09:15 PM
CAS classification : [[_linear, `class A`]]

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

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

ode:=y(t)+diff(y(t),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: 0.08 (sec). Leaf size: 24

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

\[ y(t)\to \sin (2 t)-2 \cos (2 t)+c_1 e^{-t} \]

✓ Sympy. Time used: 0.148 (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)
 

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