82.9.2 problem Ex. 2

Internal problem ID [18675]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Exercises at page 26
Problem number : Ex. 2
Date solved : Thursday, March 13, 2025 at 12:36:59 PM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Maple. Time used: 0.323 (sec). Leaf size: 40

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

\[ y \left (x \right ) = {\left (\frac {1}{x \operatorname {RootOf}\left (12 x^{4} \textit {\_Z}^{26}+x^{4} \textit {\_Z}^{16}-5 \,{\mathrm e}^{4 c_{1}}\right )^{13}}\right )}^{{2}/{3}} {\mathrm e}^{\frac {4 c_{1}}{3}} \]

✓ Mathematica. Time used: 60.22 (sec). Leaf size: 8672

ode=(2*x^2*y[x]-3*y[x]^4)+(3*x^3+2*x*y[x]^3)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Too large to display

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**2*y(x) + (3*x**3 + 2*x*y(x)**3)*Derivative(y(x), x) - 3*y(x)**4,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-2*x**2 + 3*y(x)**3)*y(x)/(x*(3*x**2 + 2*y(x)**3)) cannot be solved by the factorable group method