4.2.19 problem 19

Internal problem ID [1147]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 19
Date solved : Tuesday, September 30, 2025 at 04:23:51 AM
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 )&=0 \\ \end{align*}

✓ Maple. Time used: 0.120 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.339 (sec). Leaf size: 16

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

\begin{align*} y(x)&\to \frac {1}{3} \arcsin \left (3 \cos ^2(x)\right ) \end{align*}

✓ Sympy. Time used: 0.527 (sec). Leaf size: 17

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): 0} 
dsolve(ode,func=y(x),ics=ics)
 

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