64.5.24 problem 24

Internal problem ID [13337]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number : 24
Date solved : Tuesday, January 28, 2025 at 05:22:48 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

\begin{align*} x \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 21

dsolve([diff(x(t),t)-x(t)=sin(2*t),x(0) = 0],x(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.085 (sec). Leaf size: 28

DSolve[{D[x[t],t]-x[t]==Sin[2*t],{x[0]==0}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to e^t \int _0^te^{-K[1]} \sin (2 K[1])dK[1] \]