50.8.3 problem 1(c)

Internal problem ID [7919]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Problems for Review and Discovery. Page 53
Problem number : 1(c)
Date solved : Sunday, March 30, 2025 at 12:37:18 PM
CAS classification : [_separable]

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

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

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

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

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 20

ode=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^{-1/x} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.255 (sec). Leaf size: 8

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

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