72.8.5 problem 6

Internal problem ID [14769]
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 : Tuesday, January 28, 2025 at 07:14:40 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

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

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

\[ y = \frac {\pi }{2}+\arctan \left (t +c_{1} \right ) \]

✓ Solution by Mathematica

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

DSolve[D[y[t],t]==Sin[y[t]]^2,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*}