64.5.24 problem 24

Internal problem ID [13266]
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 : Monday, March 31, 2025 at 07:44:20 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*}

✓ Maple. Time used: 0.023 (sec). Leaf size: 21

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

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

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

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

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

✓ Sympy. Time used: 0.166 (sec). Leaf size: 24

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

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