82.9.2 problem Ex. 2

Internal problem ID [18683]
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 : Monday, March 31, 2025 at 05:57:20 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: 0.484 (sec). Leaf size: 247

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);
 

\begin{align*} y &= \frac {\operatorname {RootOf}\left (12 x^{4} \textit {\_Z}^{26} c_1^{2}+x^{4} \textit {\_Z}^{16} c_1^{2}-5\right )^{2} c_1^{2} 5^{{1}/{3}} {\left (\frac {12 \operatorname {RootOf}\left (12 x^{4} \textit {\_Z}^{26} c_1^{2}+x^{4} \textit {\_Z}^{16} c_1^{2}-5\right )^{10}+1}{c_1^{2}}\right )}^{{2}/{3}} x^{2}}{5} \\ y &= \frac {\operatorname {RootOf}\left (12 x^{4} \textit {\_Z}^{26} c_1^{2}+x^{4} \textit {\_Z}^{16} c_1^{2}-5\right )^{2} c_1^{2} 5^{{1}/{3}} {\left (\frac {12 \operatorname {RootOf}\left (12 x^{4} \textit {\_Z}^{26} c_1^{2}+x^{4} \textit {\_Z}^{16} c_1^{2}-5\right )^{10}+1}{c_1^{2}}\right )}^{{2}/{3}} \left (1+i \sqrt {3}\right )^{2} x^{2}}{20} \\ y &= \frac {\operatorname {RootOf}\left (12 x^{4} \textit {\_Z}^{26} c_1^{2}+x^{4} \textit {\_Z}^{16} c_1^{2}-5\right )^{2} c_1^{2} 5^{{1}/{3}} {\left (\frac {12 \operatorname {RootOf}\left (12 x^{4} \textit {\_Z}^{26} c_1^{2}+x^{4} \textit {\_Z}^{16} c_1^{2}-5\right )^{10}+1}{c_1^{2}}\right )}^{{2}/{3}} \left (i \sqrt {3}-1\right )^{2} x^{2}}{20} \\ \end{align*}

✓ 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