62.12.28 problem Ex 29

Internal problem ID [12803]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 19. Summary. Page 29
Problem number : Ex 29
Date solved : Monday, March 31, 2025 at 07:09:14 AM
CAS classification : [_rational]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

Timed Out