81.16.1 problem 20-1

Internal problem ID [21730]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 20. Adjoint of a differential equation. Page 506
Problem number : 20-1
Date solved : Thursday, October 02, 2025 at 08:01:29 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} \left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x^{2}+4 x -3\right ) y^{\prime }+8 y x&=1 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 26

ode:=(x^2-x)*diff(diff(y(x),x),x)+(2*x^2+4*x-3)*diff(y(x),x)+8*x*y(x) = 1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\frac {c_2}{x^{2}}+{\mathrm e}^{-2 x} c_1 +\frac {x}{6}-\frac {1}{4}}{\left (x -1\right )^{2}} \]

✓ Mathematica. Time used: 0.05 (sec). Leaf size: 35

ode=(x^2-x)*D[y[x],{x,2}]+(2*x^2+4*x-3)*D[y[x],x]+8*x*y[x]==1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {\frac {12 c_1}{x^2}+2 x+6 c_2 e^{-2 x}-3}{12 (x-1)^2} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(8*x*y(x) + (x**2 - x)*Derivative(y(x), (x, 2)) + (2*x**2 + 4*x - 3)*Derivative(y(x), x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-x**2*Derivative(y(x), (x, 2)) - 8*x*y(x) + x*Derivative(y(x), (x, 2)) + 1)/(2*x**2 + 4*x - 3) cannot be solved by the factorable group method