23.3.112 problem 114

Internal problem ID [5826]
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 : 114
Date solved : Tuesday, September 30, 2025 at 02:03:47 PM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

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

\[ y = {\mathrm e}^{x} \left (\operatorname {erf}\left (\frac {i \sqrt {2}\, \left (x -2\right )}{2}\right ) c_1 +c_2 \right ) \]

✓ Mathematica. Time used: 0.054 (sec). Leaf size: 39

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

✗ Sympy

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

False