Question
Given y = x^a + x^-b, find positive integers a and b such that x^2y’’ + 2xy’ = 12y
Answers
Bot
a = 4 and b = 2
mathhelper
nope, the stated answers don't even satisfy the required conditions.
oobleck
AAAaannndd the bot gets it wrong yet again!
you have
y' = ax^(a-1) - bx^(-b-1)
y" = a(a-1)x^(a-2) + b(b+1)x^(-b-2)
so
x^2y" + 2xy' = a(a+1)x^a + b(b-1)x^-b
That gives a=3, b=4
you have
y' = ax^(a-1) - bx^(-b-1)
y" = a(a-1)x^(a-2) + b(b+1)x^(-b-2)
so
x^2y" + 2xy' = a(a+1)x^a + b(b-1)x^-b
That gives a=3, b=4