23.1.154 problem 155 (a)

Internal problem ID [4761]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 155 (a)
Date solved : Tuesday, September 30, 2025 at 08:30:44 AM
CAS classification : [_separable]

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

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

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

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

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 16

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

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

✓ Sympy. Time used: 0.074 (sec). Leaf size: 29

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

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