76.1.27 problem 27

Internal problem ID [17255]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.1 (Separable equations). Problems at page 44
Problem number : 27
Date solved : Monday, March 31, 2025 at 03:46:41 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (\frac {\pi }{2}\right )&=\frac {\pi }{3} \end{align*}

✓ Maple. Time used: 0.131 (sec). Leaf size: 19

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

\[ y = -\frac {\arcsin \left (\frac {3}{2}+\frac {3 \cos \left (2 x \right )}{2}\right )}{3}+\frac {\pi }{3} \]

✗ Mathematica

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

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✓ Sympy. Time used: 0.756 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = - \frac {\operatorname {asin}{\left (\frac {3 \cos {\left (2 x \right )}}{2} + \frac {3}{2} \right )}}{3} + \frac {\pi }{3} \]