29.12.8 problem 327

Internal problem ID [4927]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 12
Problem number : 327
Date solved : Sunday, March 30, 2025 at 04:15:10 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: 0.027 (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: 0.296 (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)
 

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