62.28.3 problem Ex 3

Internal problem ID [12871]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter VII, Linear differential equations with constant coefficients. Article 51. Cauchy linear equation. Page 114
Problem number : Ex 3
Date solved : Wednesday, March 05, 2025 at 08:49:01 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }+y&=\frac {1}{\left (1-x \right )^{2}} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 22

ode:=x^2*diff(diff(y(x),x),x)+3*x*diff(y(x),x)+y(x) = 1/(1-x)^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\ln \left (x \right ) c_{1} +\ln \left (x \right )-\ln \left (x -1\right )+c_{2}}{x} \]

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 27

ode=x^2*D[y[x],{x,2}]+3*x*D[y[x],x]+y[x]==1/(1-x)^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {-\log (1-x)+\log (x)+c_2 \log (x)+c_1}{x} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + 3*x*Derivative(y(x), x) + y(x) - 1/(1 - x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-x**4*Derivative(y(x), (x, 2)) + 2*x**3*Derivative(y(x), (x, 2)) - x**2*y(x) - x**2*Derivative(y(x), (x, 2)) + 2*x*y(x) - y(x) + 1)/(3*x*(x**2 - 2*x + 1)) cannot be solved by the factorable group method