34.3.26 problem 25 (k)

Internal problem ID [7917]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary problems. Page 33
Problem number : 25 (k)
Date solved : Tuesday, September 30, 2025 at 05:10:02 PM
CAS classification : [_rational]

\begin{align*} y+x^{3} y+2 x^{2}+\left (x +4 x y^{4}+8 y^{3}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.014 (sec). Leaf size: 25

ode:=y(x)+x^3*y(x)+2*x^2+(x+4*x*y(x)^4+8*y(x)^3)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ -\frac {x^{3}}{3}-\ln \left (x y+2\right )-y^{4}+c_1 = 0 \]

✓ Mathematica. Time used: 0.119 (sec). Leaf size: 25

ode=(y[x]+x^3*y[x]+2*x^2)+(x+4*x*y[x]^4+8*y[x]^3)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {x^3}{3}+y(x)^4+\log (x y(x)+2)=c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*y(x) + 2*x**2 + (4*x*y(x)**4 + x + 8*y(x)**3)*Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out