54.1.180 problem 183

Internal problem ID [11494]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 183
Date solved : Tuesday, September 30, 2025 at 08:42:56 PM
CAS classification : [_separable]

\begin{align*} \left (2 x^{4}-x \right ) y^{\prime }-2 \left (x^{3}-1\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

ode:=(2*x^4-x)*diff(y(x),x)-2*(x^3-1)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \,x^{2}}{\left (2 x^{3}-1\right )^{{1}/{3}}} \]

✓ Mathematica. Time used: 0.074 (sec). Leaf size: 42

ode=(2*x^4-x)*D[y[x],x] - 2*(x^3-1)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 \exp \left (\int _1^x\frac {2-2 K[1]^3}{K[1]-2 K[1]^4}dK[1]\right )\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.179 (sec). Leaf size: 17

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

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