Question

d^2y/dx^2-5(dy/dx) +6y=0​

Answer 1

Answer:

Given equation is (D2 – 5D + 6)y = 0 A.E. is m2 – 5m + 6 = 0 i.e., (m – 2) (m – 3) = 0 i.e., m = 2, 3 ∴ m1 = 2, m2 = 3 ∴ The roots are real and distinct. ∴ The general solution of the equation is y = C1e2x + C2e3x.Read more on Sarthaks.com - https://www.sarthaks.com/364212/solve-d-2y-dx-2-5dy-dx-6y-0

Answer 2

Given equation is (D ^ 2 - 5D + 6) * y = 0

A.E. is m ^ 2 - 5m + 6 = 0

i.e., (m - 2)(m - 3) = 0

i.e., m = 2, 3

m1= 2, m2 = 3

.: The roots are real and distinct.

:. The general solution of the equation is

y = C1e^2x + C2e^3x