75.6.11 problem 11

Internal problem ID [19979]
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, October 02, 2025 at 05:04:43 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);
 

\[ y = \frac {c_1 \ln \left (x -1\right )+c_2}{x} \]

✓ Mathematica. Time used: 0.039 (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]
 

\begin{align*} y(x)&\to \frac {\sqrt {x-1} (c_2 \log (x-1)+c_1)}{\sqrt {1-x} x} \end{align*}

✗ 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