75.7.10 problem 185

Internal problem ID [16732]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 7, Total differential equations. The integrating factor. Exercises page 61
Problem number : 185
Date solved : Monday, March 31, 2025 at 03:14:03 PM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.037 (sec). Leaf size: 19

ode:=(y(x)+sin(x)*cos(x*y(x))^2)/cos(x*y(x))^2+(x/cos(x*y(x))^2+sin(y(x)))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \tan \left (x y\right )-\cos \left (x \right )-\cos \left (y\right )+c_1 = 0 \]

✗ Mathematica

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

Not solved

✗ Sympy

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

Timed Out