60.1.127 problem 130

Internal problem ID [10141]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 130
Date solved : Sunday, March 30, 2025 at 03:19:43 PM
CAS classification : [_linear]

\begin{align*} 2 x y^{\prime }-y-2 x^{3}&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

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

\[ y = \frac {2 x^{3}}{5}+\sqrt {x}\, c_1 \]

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 21

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

\[ y(x)\to \frac {2 x^3}{5}+c_1 \sqrt {x} \]

✓ Sympy. Time used: 0.265 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = C_{1} \sqrt {x} + \frac {2 x^{3}}{5} \]