83.9.7 problem 7

Internal problem ID [21965]
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. X at page 57
Problem number : 7
Date solved : Thursday, October 02, 2025 at 08:20:15 PM
CAS classification : [_exact, _rational]

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

With initial conditions

\begin{align*} y \left (2\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.685 (sec). Leaf size: 735

ode:=3*x^2-2*x*y(x)+(4*y(x)^3-x^2)*diff(y(x),x) = 0; 
ic:=[y(2) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✗ Mathematica

ode=(3*x^2-2*x*y[x])+(4*y[x]^3-x^2)*D[y[x],x]==0; 
ic={y[2]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x**2 - 2*x*y(x) + (-x**2 + 4*y(x)**3)*Derivative(y(x), x),0) 
ics = {y(2): 1} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out