12.2.5 problem 5

Internal problem ID [1541]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Linear first order. Section 2.1 Page 41
Problem number : 5
Date solved : Saturday, March 29, 2025 at 10:58:13 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 10

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

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

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 18

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

\begin{align*} y(x)\to c_1 e^{\frac {1}{x}} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.261 (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)
 

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