solve the differential equation y''-3y'-4y=2sinx using method of undetermined coefficients.

Answer 1

Solution:
Let y = A sinx + B cosx

y' = A cosx - B sinx

y'' = -A sinx - B cosx

Substituting these values in the differential equation, we get

-A sinx - B cosx - 3A cosx + 3B sinx - 4A sinx - 4B cosx = 2sinx

Simplifying, we get

-5A sinx - 5B cosx = 2sinx

Comparing coefficients, we get

A = 2/5
B = 0

Therefore, the solution of the differential equation is

y = (2/5)sinx

Answer 2

AAAaannndd the bot gets it wrong yet again!

y = c1 e^-x + c2 e^(4x) + (3cosx - 5sinx)/17