78.1.42 problem 4 (d)

Internal problem ID [18097]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 4 (d)
Date solved : Tuesday, January 28, 2025 at 11:26:12 AM
CAS classification : [_separable]

\begin{align*} 3 \cos \left (3 x \right ) \cos \left (2 y\right )-2 \sin \left (3 x \right ) \sin \left (2 y\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (\frac {\pi }{12}\right )&=\frac {\pi }{8} \end{align*}

✓ Solution by Maple

Time used: 1.204 (sec). Leaf size: 21

dsolve([3*cos(3*x)*cos(2*y(x))-2*sin(3*x)*sin(2*y(x))*diff(y(x),x)=0,y(1/12*Pi) = 1/8*Pi],y(x), singsol=all)
 

\[ y = \frac {\pi }{4}-\frac {\arctan \left (\frac {1}{\sqrt {1-2 \cos \left (6 x \right )}}\right )}{2} \]

✓ Solution by Mathematica

Time used: 6.280 (sec). Leaf size: 18

DSolve[{3*Cos[3*x]*Cos[2*y[x]]-2*Sin[3*x]*Sin[2*y[x]]*D[y[x],x]==0,{y[Pi/12]==Pi/8}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} \arccos \left (\frac {1}{2} \csc (3 x)\right ) \]