72.8.5 problem 6

Internal problem ID [14698]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Review Exercises for chapter 1. page 136
Problem number : 6
Date solved : Monday, March 31, 2025 at 12:54:07 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 12

ode:=diff(y(t),t) = sin(y(t))^2; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {\pi }{2}+\arctan \left (t +c_1 \right ) \]

✓ Mathematica. Time used: 0.253 (sec). Leaf size: 37

ode=D[y[t],t]==Sin[y[t]]^2; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{\cos (2 K[1])-1}dK[1]\&\right ]\left [-\frac {t}{2}+c_1\right ] \\ y(t)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.180 (sec). Leaf size: 10

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

\[ y{\left (t \right )} = - \operatorname {atan}{\left (\frac {1}{C_{1} + t} \right )} \]