Thread: Second order homogenous DE - Tricky

I started by trying to find the auxillary equation, as this is a homogenous second order DE.

I get to this:

k^2 - 2k + 1 + E^2


What can I do from here? (k-1)(k-1) + E^2 ???

Originally Posted by chr91

I started by trying to find the auxillary equation, as this is a homogenous second order DE.

I get to this:

k^2 - 2k + 1 + E^2


What can I do from here? (k-1)(k-1) + E^2 ???

For part a you are on the right path



Now write down the solution and see what happens as

For part b put the equation in standard form and solve. Then take the limits

Originally Posted by TheEmptySet

For part a you are on the right path



Now write down the solution and see what happens as

For part b put the equation in standard form and solve. Then take the limits

Thanks, so for a, the complementary function is y = e^x (A cos E x + B sin E x)

But I'm finding it hard to find the values for A and B to find the general solution.

For example y = e^x (A cos E x + B sin E x) and x=0, y=1

1 = 1(AcosE)

So A = 1/cosE ?


EDIT : it's k = 1+or- E