example find the general solution to the

Question

Example: Find the general solution to the subsequent differential equation.

x²y′′ - 7 xy′ + 16 y= 0

 Solution

First the roots of (3)

 r (r -1) - 7r + 16= 0

r² - 8r + 16 = 0

(r - 4)² = 0       ⇒ r =4

Therefore the general solution is,

 y(x) = c₁ x⁴ + c₂ x⁴ In x