11.2.5 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 : Tuesday, September 30, 2025 at 06:38:05 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*}

✓ Maple. Time used: 0.037 (sec). Leaf size: 23

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

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

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 31

ode=D[y[t],t]==Sin[t]^2; 
ic=y[Pi/6]==3; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.097 (sec). Leaf size: 26

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-sin(t)**2 + Derivative(y(t), t),0) 
ics = {y(pi/6): 3} 
dsolve(ode,func=y(t),ics=ics)
 

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