90.4.7 problem 8

Internal problem ID [25102]
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 : 8
Date solved : Thursday, October 02, 2025 at 11:50:14 PM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

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

\[ y = -\frac {\cos \left (t \right )}{5}+\frac {2 \sin \left (t \right )}{5}+{\mathrm e}^{-2 t} c_1 \]

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 26

ode=D[y[t],{t,1}] +2*y[t] == Sin[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {2 \sin (t)}{5}-\frac {\cos (t)}{5}+c_1 e^{-2 t} \end{align*}

✓ Sympy. Time used: 0.075 (sec). Leaf size: 20

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

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