59.1.5 problem 5.1 (v)

Internal problem ID [14989]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 5, Trivial differential equations. Exercises page 33
Problem number : 5.1 (v)
Date solved : Thursday, October 02, 2025 at 09:58:07 AM
CAS classification : [_quadrature]

\begin{align*} T^{\prime }&={\mathrm e}^{-t} \sin \left (2 t \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 25

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

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

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 28

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

\begin{align*} T(t)&\to -\frac {1}{5} e^{-t} (\sin (2 t)+2 \cos (2 t))+c_1 \end{align*}

✓ Sympy. Time used: 0.096 (sec). Leaf size: 26

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

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