23.3.236 problem 238

Internal problem ID [5950]
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 : 238
Date solved : Tuesday, September 30, 2025 at 02:06:43 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (3-x \right ) y-\left (4-3 x \right ) y^{\prime }+\left (1-2 x \right ) y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.038 (sec). Leaf size: 31

ode:=(-x+3)*y(x)-(4-3*x)*diff(y(x),x)+(1-2*x)*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\sqrt {2}\, \left (\left (\frac {c_1}{4}+c_2 \right ) \Gamma \left (-\frac {1}{4}, -\frac {1}{4}+\frac {x}{2}\right )+\Gamma \left (\frac {3}{4}\right ) c_1 \right ) {\mathrm e}^{x -\frac {1}{4}}}{2} \]

✓ Mathematica. Time used: 0.159 (sec). Leaf size: 47

ode=(3 - x)*y[x] - (4 - 3*x)*D[y[x],x] + (1 - 2*x)*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {e^{x-\frac {1}{2}} \left (\sqrt [4]{2} c_2 \Gamma \left (-\frac {1}{4},\frac {1}{4} (2 x-1)\right )-8 c_1\right )}{4\ 2^{3/8}} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((1 - 2*x)*Derivative(y(x), (x, 2)) + (3 - x)*y(x) - (4 - 3*x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False