Put the given differential equation into form (3) in Section 6.3 (x − x0)2y'' + (x − x0)p(x)y' + q(x)y = 0 (3) for each regular singular point of the equation. Identify the functions p(x) and q(x). (x2 − 1)y'' + 3(x + 1)y' + (x2 − x)y = 0

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.

sina-sinb

cosb+cosa

tana-tanb

cos0+cos x pi/3

20tan

step-by-step explanation:

um is there supposed to be a picture?