25.1.6 problem 6

Internal problem ID [4218]
Book : Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section : Chapter 11.3, page 316
Problem number : 6
Date solved : Monday, January 27, 2025 at 08:42:41 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=3 \cos \left (y\right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 12

dsolve(diff(y(x),x)=3*cos(y(x))^2,y(x), singsol=all)
 

\[ y \left (x \right ) = \arctan \left (3 x +3 c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.358 (sec). Leaf size: 32

DSolve[D[y[x],x]==3*Cos[y[x]]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \arctan (3 x+2 c_1) \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}