23.1.740 problem 740

Internal problem ID [5347]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 740
Date solved : Tuesday, September 30, 2025 at 12:32:59 PM
CAS classification : unknown

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

✓ Maple. Time used: 0.039 (sec). Leaf size: 33

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

\[ \frac {\left (-2 \sin \left (A \right ) \sin \left (x \right )+\cos \left (y\right )\right ) \sin \left (y\right )}{2}+\frac {\cos \left (x \right ) \sin \left (x \right )}{2}+\frac {x}{2}+c_1 +\frac {y}{2} = 0 \]

✓ Mathematica. Time used: 0.348 (sec). Leaf size: 162

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

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

✗ Sympy

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

Timed Out