59.3.7 problem 8.3

Internal problem ID [15006]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 8, Separable equations. Exercises page 72
Problem number : 8.3
Date solved : Thursday, October 02, 2025 at 09:58:26 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 9

ode:=x*diff(y(x),x) = k*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,x^{k} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 16

ode=x*D[y[x],x]==k*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.076 (sec). Leaf size: 29

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

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