23.3.418 problem 423

Internal problem ID [6132]
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 : 423
Date solved : Tuesday, September 30, 2025 at 02:22:05 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 19

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

\[ y = {\mathrm e}^{x} \left (c_1 x -\ln \left (-1+x \right )+c_2 -1\right ) \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 23

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

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

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - (x**2*y(x) + x**2*Derivative(y(x), (x, 2))