Internal problem ID [11655]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {x^{\prime }=2 \sin \left (t \right )^{2}} \] With initial conditions \begin {align*} \left [x \left (\frac {\pi }{4}\right ) = \frac {\pi }{4}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.0 (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: 0.01 (sec). Leaf size: 16
DSolve[{x'[t]==2*Sin[t]^2,{x[Pi/4]==Pi/4}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to t-\sin (t) \cos (t)+\frac {1}{2} \]