17.2.5 problem 1.1-3 (e)

Internal problem ID [3429]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.1-3, page 6
Problem number : 1.1-3 (e)
Date solved : Monday, January 27, 2025 at 07:36:25 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (\frac {\pi }{6}\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 23

dsolve([diff(y(t),t)=sin(t)^2,y(1/6*Pi) = 3],y(t), singsol=all)
 

\[ y = \frac {t}{2}+3-\frac {\pi }{12}+\frac {\sqrt {3}}{8}-\frac {\sin \left (2 t \right )}{4} \]

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 31

DSolve[{D[y[t],t]==Sin[t]^2,y[Pi/6]==3},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{24} \left (3 \left (4 t+\sqrt {3}+24\right )-6 \sin (2 t)-2 \pi \right ) \]