87.13.12 problem 12

Internal problem ID [23495]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 100
Problem number : 12
Date solved : Thursday, October 02, 2025 at 09:42:26 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

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

\[ y = \left (x -2\right ) \left (c_2 \ln \left (x -2\right )+c_1 \right ) \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 19

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

\begin{align*} y(x)&\to (x-2) (c_2 \log (x-2)+c_1) \end{align*}

✓ Sympy. Time used: 0.147 (sec). Leaf size: 7

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

\[ y{\left (x \right )} = C_{1} \left (x - 2\right ) \]