23.2.304 problem 325

Internal problem ID [5659]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 325
Date solved : Friday, October 03, 2025 at 01:40:15 AM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} x^{4} {y^{\prime }}^{3}-x^{3} y {y^{\prime }}^{2}-x^{2} y^{2} y^{\prime }+x y^{3}&=1 \end{align*}

✓ Maple. Time used: 1.044 (sec). Leaf size: 686

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

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

✓ Mathematica. Time used: 61.254 (sec). Leaf size: 67473

ode=x^4 (D[y[x],x])^3 -x^3 y[x] (D[y[x],x])^2 - x^2 y[x]^2 D[y[x],x]+x y[x]^3==1; 
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(x**4*Derivative(y(x), x)**3 - x**3*y(x)*Derivative(y(x), x)**2 - x**2*y(x)**2*Derivative(y(x), x) + x*y(x)**3 - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out