68.5.40 problem 47

Internal problem ID [17291]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number : 47
Date solved : Thursday, October 02, 2025 at 02:01:00 PM
CAS classification : [[_linear, `class A`]]

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

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

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

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

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 31

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

\begin{align*} y(t)&\to e^t \left (\int _1^te^{-K[1]} \sin (2 K[1])dK[1]+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.085 (sec). Leaf size: 22

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

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