28.1.52 problem 53

Internal problem ID [4358]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 53
Date solved : Sunday, March 30, 2025 at 03:10:15 AM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Maple. Time used: 0.522 (sec). Leaf size: 149

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

\[ y = \frac {-x^{{3}/{2}} \operatorname {RootOf}\left (-16+x^{7} c_1 \,\textit {\_Z}^{12}-4 c_1 \,x^{{11}/{2}} \textit {\_Z}^{10}+6 c_1 \,x^{4} \textit {\_Z}^{8}+\left (128 x^{{9}/{2}}-4 c_1 \,x^{{5}/{2}}\right ) \textit {\_Z}^{6}+\left (-192 x^{3}+c_1 x \right ) \textit {\_Z}^{4}+96 x^{{3}/{2}} \textit {\_Z}^{2}\right )^{2}+1}{2 \operatorname {RootOf}\left (-16+x^{7} c_1 \,\textit {\_Z}^{12}-4 c_1 \,x^{{11}/{2}} \textit {\_Z}^{10}+6 c_1 \,x^{4} \textit {\_Z}^{8}+\left (128 x^{{9}/{2}}-4 c_1 \,x^{{5}/{2}}\right ) \textit {\_Z}^{6}+\left (-192 x^{3}+c_1 x \right ) \textit {\_Z}^{4}+96 x^{{3}/{2}} \textit {\_Z}^{2}\right )^{2}} \]

✓ Mathematica. Time used: 60.168 (sec). Leaf size: 2023

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

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

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

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