83.3.1 problem 1

Internal problem ID [18986]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (B) at page 9
Problem number : 1
Date solved : Monday, March 31, 2025 at 06:28:34 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.062 (sec). Leaf size: 25

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

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

✓ Mathematica. Time used: 0.591 (sec). Leaf size: 55

ode=x*Cos[y[x]]^2==y[x]*Cos[x]^2*D[y[x],x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\frac {1}{2} (\text {$\#$1} \tan (\text {$\#$1})+\log (\cos (\text {$\#$1})))\&\right ]\left [\frac {1}{2} (x \tan (x)+\log (\cos (x)))+c_1\right ] \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}

✗ Sympy

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

Timed Out