Next time check that your post displays latex equations properly.

above is the given equation based on Kirchhoff law.

And the question is:

Find the solution of the ODE to obtain y[t] as some integral of x[t].

I had search through google and found a solution here.

But i do not know how to introduced the !! Anyone help!! can any1 provide me some solution??

The ODe of the electric circuit is:

multiply the equation by:

as you might notice the left hand side became a perfect differential. Now we integrate both sides from to arbitrary time t:

# RC is the time constant of the circuit which is usually denoted as

# This integral is called the convolution integral, and

is the impulse response of the circuit, these are very important concepts which you'll probably meet in your future studies.