74.4.11 problem 11

Internal problem ID [15833]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 11
Date solved : Monday, March 31, 2025 at 01:57:29 PM
CAS classification : [_separable]

\begin{align*} 3 \sin \left (x \right )-4 \cos \left (y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 13

ode:=3*sin(x)-4*cos(y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \arcsin \left (-\frac {3 \cos \left (x \right )}{4}+\frac {3 c_1}{4}\right ) \]

✓ Mathematica. Time used: 0.232 (sec). Leaf size: 35

ode=3*Sin[x]-4*Cos[y[x]]*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\cos (K[1])dK[1]\&\right ]\left [\int _1^x\frac {3}{4} \sin (K[2])dK[2]+c_1\right ] \]

✓ Sympy. Time used: 0.574 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*sin(x) - 4*cos(y(x))*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = \pi - \operatorname {asin}{\left (C_{1} - \frac {3 \cos {\left (x \right )}}{4} \right )}, \ y{\left (x \right )} = \operatorname {asin}{\left (C_{1} - \frac {3 \cos {\left (x \right )}}{4} \right )}\right ] \]