ODE

Obtain the general solution of the following DEs:

i. y′′′ + y′′ − 4y′ + 2y = 0

ii. y(4) + 4y(2) = 0

iii. x(x − 2)y′′ + 2(x − 1)y′ − 2y = 0; use y1 = (1 − x)

iv. y′′ − 4y = sin2(x)

v. y′′ − 4y′ + 3y = x ; use y1 = e3x

vi. y′′ + 5y′ + 6y = e2xcos(x)

vii. y′′ + y = sec(x) tan(x)