77.1.112 problem 140 (page 204)

Internal problem ID [17931]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 140 (page 204)
Date solved : Monday, March 31, 2025 at 04:51:46 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+\frac {x y^{\prime }}{1-x}-\frac {y}{1-x}&=x -1 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 18

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

\[ y = c_2 x +{\mathrm e}^{x} c_1 -x^{2}-1 \]

✓ Mathematica. Time used: 0.04 (sec). Leaf size: 25

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

\[ y(x)\to -x^2-(1+c_2) x+c_1 e^x-1 \]

✗ Sympy

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

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