84.5.6 problem 3.2 (b)

Internal problem ID [22093]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 3. Classification of first-order differential equations. Solved problems. Page 11
Problem number : 3.2 (b)
Date solved : Thursday, October 02, 2025 at 08:23:55 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 12

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

\[ y = \frac {1}{-\ln \left (x \right )+c_1} \]

✓ Mathematica. Time used: 0.071 (sec). Leaf size: 19

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

\begin{align*} y(x)&\to -\frac {1}{\log (x)+c_1}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.079 (sec). Leaf size: 10

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

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