44.8.8 problem 1(h)

Internal problem ID [9210]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Problems for Review and Discovery. Page 53
Problem number : 1(h)
Date solved : Tuesday, September 30, 2025 at 06:14:44 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.043 (sec). Leaf size: 9

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

\[ y = \arcsin \left (c_1 \sec \left (x \right )\right ) \]

✓ Mathematica. Time used: 0.056 (sec). Leaf size: 80

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

\[ \text {Solve}\left [\int _1^x(\cos (K[1]+y(x))-\cos (K[1]-y(x)))dK[1]+\int _1^{y(x)}\left (\cos (x-K[2])+\cos (x+K[2])-\int _1^x(-\sin (K[1]-K[2])-\sin (K[1]+K[2]))dK[1]\right )dK[2]=c_1,y(x)\right ] \]

✓ Sympy. Time used: 0.321 (sec). Leaf size: 19

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

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