23.1.20 problem 2(j)

Internal problem ID [4110]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 2. First order equations. Exercises at page 14
Problem number : 2(j)
Date solved : Tuesday, March 04, 2025 at 05:26:22 PM
CAS classification : [_separable]

\begin{align*} 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{align*}

With initial conditions

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

✓ Maple. Time used: 0.374 (sec). Leaf size: 21

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

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

✓ Mathematica. Time used: 6.682 (sec). Leaf size: 18

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

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

✓ Sympy. Time used: 0.750 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*sin(3*x)*sin(2*y(x))*Derivative(y(x), x) - 3*cos(3*x)*cos(2*y(x)),0) 
ics = {y(pi/12): pi/8} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {\operatorname {acos}{\left (\frac {1}{2 \sin {\left (3 x \right )}} \right )}}{2} \]