Finding Solution to 2nd Order Diff Eq at x=1

[zerafachris]

Homework Statement

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.

 

[vela]

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