29.13.19 problem 373

Internal problem ID [4973]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 13
Problem number : 373
Date solved : Tuesday, March 04, 2025 at 07:39:38 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

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

\[ y \left (x \right ) = \frac {-x^{2}+c_{1}}{x^{4}-x} \]

✓ Mathematica. Time used: 0.044 (sec). Leaf size: 21

ode=x(1-x^3)D[y[x],x]==2 x-(1-4 x^3)y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {x^2+c_1}{x-x^4} \]

✓ Sympy. Time used: 0.289 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(1 - x**3)*Derivative(y(x), x) - 2*x + (1 - 4*x**3)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} - x^{2}}{x \left (x^{3} - 1\right )} \]