# Thread: second order differential eq help

1. ## second order differential eq help

hi can any body help with the answer to this?

(d^2x/dy^2)+16x=16y

How does this compare to a general second order equation?
Are you able to predict the response x(t) when y(t) is a unit step change?
Solve for x(t) to verify your prediction.

any help would be appreciated.

2. Originally Posted by al2308
hi can any body help with the answer to this?

(d^2x/dy^2)+16x=16y

How does this compare to a general second order equation?
Are you able to predict the response x(t) when y(t) is a unit step change?
Solve for x(t) to verify your prediction.

any help would be appreciated.
yes, it compares to the geenral second order ODE. just take the middle term in your characteristic equation to be zero

3. Ok,

M^2 = -16

so M=+/- j4

which means

Xc= Acos4X + BSin4X

for Xp

16Xp=16y=16
Xp=1

x= 1 + Acos4x + Bsin4X

x(0) = 1 + A + B

X'(0) = -2Asin4x +2Bcos4x

is this correct?

4. Originally Posted by al2308
Ok,

M^2 = -16

so M=+/- j4

which means

Xc= Acos4X + BSin4X

for Xp

16Xp=16y=16
Xp=1

x= 1 + Acos4x + Bsin4X

x(0) = 1 + A + B

X'(0) = -2Asin4x +2Bcos4x

is this correct?
Clearly your Xp does not work - did you check it by substitution into the DE?

Xp = 16y.