23.1.244 problem 239

Internal problem ID [4851]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 239
Date solved : Tuesday, September 30, 2025 at 08:44:20 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.000 (sec). Leaf size: 15

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

\[ y = \frac {2 x^{3}}{7}+\frac {c_1}{\sqrt {x}} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 21

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

\begin{align*} y(x)&\to \frac {2 x^3}{7}+\frac {c_1}{\sqrt {x}} \end{align*}

✓ Sympy. Time used: 0.111 (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)
 

\[ y{\left (x \right )} = \frac {C_{1}}{\sqrt {x}} + \frac {2 x^{3}}{7} \]