Calculus Problem

Question

Solve the differential equation .

Answer 1

If the problem is

(1/8x)(dy/dx) = y(4x² - 1)^(1/2) then dy/y = 8x(4x² - 1)^(1/2)

Integrating, we have lny = (2/3)(4x² - 1)^(3/2)

Assume the constant of integration = 0, then taking each side to the e power, we have

y = exp{ (2/3)(4x² - 1)^(3/2) }