62.10.3 problem Ex 3

Internal problem ID [12769]
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 : Monday, March 31, 2025 at 07:03:46 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: 0.25 (sec). Leaf size: 129

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]
 

\[ \text {Solve}\left [x=\exp \left (\int _1^{y(x)}\frac {K[1]^3-4}{-K[1]^4-2 K[1]}dK[1]\right ) \int _1^{y(x)}\frac {2 \exp \left (-\int _1^{K[2]}\frac {K[1]^3-4}{-K[1]^4-2 K[1]}dK[1]\right ) K[2]^4}{-K[2]^4-2 K[2]}dK[2]+c_1 \exp \left (\int _1^{y(x)}\frac {K[1]^3-4}{-K[1]^4-2 K[1]}dK[1]\right ),y(x)\right ] \]

✓ Sympy. Time used: 103.764 (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)
 

\[ \text {Solution too large to show} \]