81.6.11 problem 11

Internal problem ID [18615]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter V. Homogeneous linear differential equations. Exact equations. Exercises at page 69
Problem number : 11
Date solved : Thursday, March 13, 2025 at 12:25:22 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} \left (x^{2}-x \right ) y^{\prime \prime }+\left (3 x -2\right ) y^{\prime }+y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

ode:=(x^2-x)*diff(diff(y(x),x),x)+(3*x-2)*diff(y(x),x)+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.053 (sec). Leaf size: 35

ode=(x^2-x)*D[y[x],{x,2}]+(3*x-2)*D[y[x],x]+y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

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

False