9.1.22 problem 22

Internal problem ID [2862]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 5, page 21
Problem number : 22
Date solved : Tuesday, September 30, 2025 at 05:55:24 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (2\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 9

ode:=x*diff(y(x),x)+2*y(x) = 0; 
ic:=[y(2) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {4}{x^{2}} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 10

ode=x*D[y[x],x]+2*y[x]==0; 
ic=y[2]==1; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {4}{x^2} \end{align*}

✓ Sympy. Time used: 0.066 (sec). Leaf size: 7

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) + 2*y(x),0) 
ics = {y(2): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {4}{x^{2}} \]