75.7.4 problem 178

Internal problem ID [16726]
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 : 178
Date solved : Monday, March 31, 2025 at 03:11:23 PM
CAS classification : [_exact]

\begin{align*} 3 x^{2} \tan \left (y\right )-\frac {2 y^{3}}{x^{3}}+\left (x^{3} \sec \left (y\right )^{2}+4 y^{3}+\frac {3 y^{2}}{x^{2}}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.021 (sec). Leaf size: 24

ode:=3*x^2*tan(y(x))-2*y(x)^3/x^3+(x^3*sec(y(x))^2+4*y(x)^3+3*y(x)^2/x^2)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ x^{3} \tan \left (y\right )+\frac {y^{3}}{x^{2}}+y^{4}+c_1 = 0 \]

✗ Mathematica

ode=(3*x^2*Tan[y[x]]-2*y[x]^3/x^3  )+( x^3*Sec[y[x]]^2+4*y[x]^3+ 3*y[x]^2/x^2 )*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(3*x**2*tan(y(x)) + (x**3/cos(y(x))**2 + 4*y(x)**3 + 3*y(x)**2/x**2)*Derivative(y(x), x) - 2*y(x)**3/x**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out