23.3.58 problem 60

Internal problem ID [5772]
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 : 60
Date solved : Tuesday, September 30, 2025 at 02:02:54 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 26

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

\[ y = {\mathrm e}^{\frac {x}{2}} \left (c_2 \operatorname {AiryBi}\left (\frac {1}{4}-x \right )+c_1 \operatorname {AiryAi}\left (\frac {1}{4}-x \right )\right ) \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 50

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

\begin{align*} y(x)&\to e^{x/2} \left (c_1 \operatorname {AiryAi}\left (\frac {1}{4} \sqrt [3]{-1} (4 x-1)\right )+c_2 \operatorname {AiryBi}\left (\frac {1}{4} \sqrt [3]{-1} (4 x-1)\right )\right ) \end{align*}

✗ Sympy

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

False