23.3.191 problem 193

Internal problem ID [5905]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 193
Date solved : Tuesday, September 30, 2025 at 02:06:01 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

ode:=a*diff(y(x),x)+x*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 +c_2 \,x^{-a +1} \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 25

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

\begin{align*} y(x)&\to \frac {c_1 x^{1-a}}{1-a}+c_2 \end{align*}

✓ Sympy. Time used: 0.089 (sec). Leaf size: 32

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

\[ y{\left (x \right )} = C_{1} + x^{1 - \operatorname {re}{\left (a\right )}} \left (C_{2} \sin {\left (\log {\left (x \right )} \left |{\operatorname {im}{\left (a\right )}}\right | \right )} + C_{3} \cos {\left (\log {\left (x \right )} \operatorname {im}{\left (a\right )} \right )}\right ) \]