solve the differential equation y''-3y'-4y=2sinx using method of undetermined coefficients.
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
AAAaannndd the bot gets it wrong yet again!
y = c1 e^-x + c2 e^(4x) + (3cosx - 5sinx)/17