# Non-homogenous 2nd Order Differential Equation using Undetermined Coefficients Method

1. Dec 19, 2011

### zerafachris

1. The problem statement, all variables and given/known data
Find the solution to the following 2nd Order Differential Equation at x = 1:
y'' = 10y -200

Boundary conditions:
when x = 0, y = 100
when x = 1, y' = 10

2. The attempt at a solution
Complimentary function: y = A exp{(10)^0.5 x} + B exp{- (10)^0.5 x}
Particular Integral: 20
General Solution: y = A exp{(10)^0.5 x} + B exp{- (10)^0.5 x} + 20
Coefficients: A = 0.276701988 B = 79.72329801
At x = 1, y = 29.91152764

My concern is whether the P.I. is correct.
P.S. I ran this diff equation in MATLAB and the solution at x = 1 was calculated to be 25.7312811548222.

Last edited: Dec 19, 2011
2. Dec 19, 2011

### vela

Staff Emeritus
Re: Non-homogenous 2nd Order Differential Equation using Undetermined Coefficients Me

Yes, it is. It's easy enough to check for yourself. Just plug it back to see if it satisfies the differential equation.