15.12.16 problem 16

Internal problem ID [3160]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 20, page 90
Problem number : 16
Date solved : Sunday, March 30, 2025 at 01:19:59 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 19

ode:=diff(diff(y(x),x),x)-2*diff(y(x),x)+y(x) = exp(x)/(1-x)^2; 
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: 0.032 (sec). Leaf size: 23

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

\[ y(x)\to e^x (-\log (x-1)+c_2 x-1+c_1) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) - 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)) - exp(x)/(1 - x)**2,0) 
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)) - 2*x*y(x) - 2*x*Derivative(y(x), (x, 2)) + y(x) - exp(x) + Derivative(y(x), (x, 2)))/(2*(x**2 - 2*x + 1)) cannot be solved by the factorable group method