65.1.5 problem 5.1 (v)

Internal problem ID [13708]
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 : Tuesday, January 28, 2025 at 05:55:44 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 27

DSolve[D[ T[t],t]==Exp[-t]*Sin[2*t],T[t],t,IncludeSingularSolutions -> True]
 

\[ T(t)\to \int _1^te^{-K[1]} \sin (2 K[1])dK[1]+c_1 \]