Internal problem ID [2512]
Book: Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section: Exercises, page 14
Problem number: 2(j).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {2 \sin \left (3 x \right ) \sin \left (2 y\right ) y^{\prime }-3 \cos \left (3 x \right ) \cos \left (2 y\right )=0} \end {gather*} With initial conditions \begin {align*} \left [y \left (\frac {\pi }{12}\right ) = \frac {\pi }{8}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.367 (sec). Leaf size: 15
dsolve([2*sin(3*x)*sin(2*y(x))*diff(y(x),x)-3*cos(3*x)*cos(2*y(x))=0,y(1/12*Pi) = 1/8*Pi],y(x), singsol=all)
\[ y \relax (x ) = \frac {\arccos \left (\frac {1}{2 \sin \left (3 x \right )}\right )}{2} \]
✓ Solution by Mathematica
Time used: 2.559 (sec). Leaf size: 16
DSolve[{2*Sin[3*x]*Sin[2*y[x]]*y'[x]-3*Cos[3*x]*Cos[2*y[x]]==0,y[Pi/12]==Pi/8},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \sec ^{-1}(2 \sin (3 x)) \\ \end{align*}