23.3.413 problem 418

Internal problem ID [6127]
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 : 418
Date solved : Tuesday, September 30, 2025 at 02:22:00 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

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

\[ y = \frac {c_1 +c_2 \left (-1+x \right )}{\left (-1+x \right )^{2}} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 20

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

\begin{align*} y(x)&\to \frac {c_1 (x-1)+c_2}{(x-1)^2} \end{align*}

✓ Sympy. Time used: 0.148 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = \frac {C_{1}}{\left (x - 1\right )^{\frac {3}{2}}} \]