83.5.8 problem 2 (c)

Internal problem ID [21943]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter III. First order differential equations of the first degree. Ex. VI at page 47
Problem number : 2 (c)
Date solved : Thursday, October 02, 2025 at 08:18:50 PM
CAS classification : [[_homogeneous, `class G`], _rational]

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

With initial conditions

\begin{align*} y \left (1\right )&=1 \\ \end{align*}

✗ Maple

ode:=y(x) = (2*x^2*y(x)^3-x)*diff(y(x),x); 
ic:=[y(1) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]==(2*x^2*y[x]^3-x)*D[y[x],x]; 
ic={y[1]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-2*x**2*y(x)**3 + x)*Derivative(y(x), x) + y(x),0) 
ics = {y(1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out