65.1.8 problem 5.4 (iii)

Internal problem ID [13632]
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 : 5.4 (iii)
Date solved : Wednesday, March 05, 2025 at 10:05:39 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} x \left (\frac {\pi }{4}\right )&=\frac {\pi }{4} \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 13

ode:=diff(x(t),t) = 2*sin(t)^2; 
ic:=x(1/4*Pi) = 1/4*Pi; 
dsolve([ode,ic],x(t), singsol=all);
 

\[ x \left (t \right ) = t +\frac {1}{2}-\frac {\sin \left (2 t \right )}{2} \]

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 29

ode=D[x[t],t]==2*Sin[t]^2; 
ic={x[Pi/4]==Pi/4}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\[ x(t)\to \int _{\frac {\pi }{4}}^t2 \sin ^2(K[1])dK[1]+\frac {\pi }{4} \]

✓ Sympy. Time used: 0.137 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-2*sin(t)**2 + Derivative(x(t), t),0) 
ics = {x(pi/4): pi/4} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = t - \sin {\left (t \right )} \cos {\left (t \right )} + \frac {1}{2} \]