23.3.210 problem 212

Internal problem ID [5924]
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 : 212
Date solved : Tuesday, September 30, 2025 at 02:06:16 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

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

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

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 17

ode=-((1 - x)*y[x]) + (1 - 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 e^x (c_2 \log (x)+c_1) \end{align*}

✗ Sympy

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

False