65.1.8 problem 5.4 (iii)

Internal problem ID [13711]
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 : Tuesday, January 28, 2025 at 05:55:47 AM
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*}

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

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

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