23.3.205 problem 207

Internal problem ID [5919]
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 : 207
Date solved : Tuesday, September 30, 2025 at 02:06:12 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 72

ode=-y[x] - (2 - x)*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 {2 e^{-x/2} \sqrt {x} \left ((c_1 x+2 i c_2) \cosh \left (\frac {x}{2}\right )-(i c_2 x+2 c_1) \sinh \left (\frac {x}{2}\right )\right )}{\sqrt {\pi } \sqrt {-i x}} \end{align*}

✗ Sympy

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

False