89.1.5 problem 5

Internal problem ID [24240]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 21
Problem number : 5
Date solved : Thursday, October 02, 2025 at 10:01:18 PM
CAS classification : [_separable]

\begin{align*} m y-n x y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

ode:=m*y(x)-n*x*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,x^{\frac {m}{n}} \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 20

ode=(m*y[x])-(n*x)*D[y[x],{x,1}]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 x^{m/n}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.088 (sec). Leaf size: 34

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

\[ y{\left (x \right )} = x^{\operatorname {re}{\left (\frac {m}{n}\right )}} \left (C_{1} \sin {\left (\log {\left (x \right )} \left |{\operatorname {im}{\left (\frac {m}{n}\right )}}\right | \right )} + C_{2} \cos {\left (\log {\left (x \right )} \operatorname {im}{\left (\frac {m}{n}\right )} \right )}\right ) \]