23.3.235 problem 237

Internal problem ID [5949]
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 : 237
Date solved : Tuesday, September 30, 2025 at 02:06:42 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Maple. Time used: 0.025 (sec). Leaf size: 54

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

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

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 50

ode=-y[x] - (2 + 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 e^{-x/2} \left (c_2 L_{-\frac {1}{4}}^{\frac {1}{4}}\left (\frac {x}{2}-\frac {1}{4}\right )+\frac {\sqrt {2} c_1}{\sqrt [4]{2 x-1}}\right ) \end{align*}

✗ Sympy

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

False