87.9.22 problem 37

Internal problem ID [23395]
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 74
Problem number : 37
Date solved : Thursday, October 02, 2025 at 09:41:01 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 24

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

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

✓ Mathematica. Time used: 0.058 (sec). Leaf size: 27

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

\begin{align*} y(x)&\to \frac {c_2 x+c_1}{(a-x) (b-x)} \end{align*}

✗ Sympy

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

False