56.10.3 problem Ex 3

Internal problem ID [14121]
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 17. Other forms which Integrating factors can be found. Page 25
Problem number : Ex 3
Date solved : Thursday, October 02, 2025 at 09:15:01 AM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

✓ Maple. Time used: 0.008 (sec). Leaf size: 27

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

\[ x -\frac {\left (-y^{2}+c_1 \right ) y^{2}}{y^{3}+2} = 0 \]

✓ Mathematica. Time used: 60.151 (sec). Leaf size: 2021

ode=(y[x]^4+2*y[x])+(x*y[x]^3+2*y[x]^4-4*x)*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. Time used: 57.324 (sec). Leaf size: 4383

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

\[ \text {Latex too large to display} \]