Unit step response of RC high pass filter

[erece]

what is the unit step response of a high pass RC filter ?
I want to calculate using transfer function approach.
My solution :
Y(s)/X(s) = RCs/(1+sRC)

X(s)=1/s
Y(s)=RC/(1+sRC)
taking inverse laplace transform we should get
y(t)=exp(-t/RC)


But if we consider Y(s)=RC/(1+sRC)
RCsY(s) + Y(s) = RC
then this is a non homogeneous equation
so the solution should contain a dc term also which is a complementary function.
but the previous solution i have written above does not contain the dc term.
Please clarify this...

 

[Enthalpy]

y(t)=exp(-t/RC)

 

[Ratch]

erece,

Please clarify this...

The inverse Laplace of RCs/(1+sRC) is Dirac(t)-exp(-t/RC)/RC, not what you posted.

Ratch