23.1.344 problem 330

Internal problem ID [4951]
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 : 330
Date solved : Tuesday, September 30, 2025 at 09:04:08 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

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

\[ y = c_1 \,{\mathrm e}^{-\frac {1}{2 x}} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 22

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

\begin{align*} y(x)&\to c_1 e^{\left .-\frac {1}{2}\right /x}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.184 (sec). Leaf size: 10

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

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