9.1.24 problem 24

Internal problem ID [2864]
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 : 24
Date solved : Tuesday, September 30, 2025 at 05:55:29 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (3\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.017 (sec). Leaf size: 14

ode:=x^2*diff(y(x),x)+y(x)^2 = 0; 
ic:=[y(3) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {3 x}{4 x -3} \]

✓ Mathematica. Time used: 0.068 (sec). Leaf size: 15

ode=x^2*D[y[x],x]+y[x]^2==0; 
ic=y[3]==1; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {3 x}{4 x-3} \end{align*}

✓ Sympy. Time used: 0.092 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), x) + y(x)**2,0) 
ics = {y(3): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \frac {x}{1 - \frac {4 x}{3}} \]