i want to know the impulse response to the following

4y''(t) = 2x(t) - x'(t)

I am able to solve this problem without the x'(t) on the right hand side but i am not sure how to deal with x'(t). The way i was told to this is to integrate it through "0 negative " to " 0 positive" thanks

 

I find a clue from my old differential equation recollection, might help you!

 

thanks.this will help..

 

Another approach might be using the Laplace Transform

or

For which the impulse response is the inverse transform of H(s), giving the output y(t) as ....[for t>=0]

\(y(t)=\frac{t}{2}-\frac{1}{4}\)

Which agrees with tgotwalt1158's solution.

 

thanks for your help...this is helpful...

 

i solved another question for impulse response
y'' + 9 y= -6x'

after doing laplace i get

Y = -6s/(s^2 + 9)


and so y(t) =-6 cos3t .

is it correct..??

 

That's correct