Internal problem ID [1949]
Book: Ordinary Differential Equations, Robert H. Martin, 1983
Section: Problem 1.1-3, page 6
Problem number: 1.1-3 (e).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-\left (\sin ^{2}\relax (t )\right )=0} \end {gather*} With initial conditions \begin {align*} \left [y \left (\frac {\pi }{6}\right ) = 3\right ] \end {align*}
✓ Solution by Maple
Time used: 0.02 (sec). Leaf size: 23
dsolve([diff(y(t),t)=sin(t)^2,y(1/6*Pi) = 3],y(t), singsol=all)
\[ y \relax (t ) = \frac {t}{2}+3-\frac {\pi }{12}+\frac {\sqrt {3}}{8}-\frac {\sin \left (2 t \right )}{4} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 31
DSolve[{y'[t]==Sin[t]^2,y[Pi/6]==3},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{24} \left (3 \left (4 t+\sqrt {3}+24\right )-6 \sin (2 t)-2 \pi \right ) \\ \end{align*}