n integro-differential equation is an equation in which the unknown dependent variable
y
appears within an integral, and its derivative
dy/dt
also appears. onsider the following initial value problem, defined for
t≥0
, of which the equation is an integro-differential equation:
dy/dt +9∫ t0 y(t−τ)e ^−6τ dτ=9,y(0)=0.
(i) Use the Convolution and Laplace transforms to find the Laplace transform of the solution and enter it below:
Y(s)=L{y(t)}=
Remarks : The definition of Convolution is covered in 3.4. Express the integration part of the above equation as a Convolution of 2 functions. (ii) Get the solution
y(t)
by finding the Inverse Laplace Transform of
Y(s)
obtained in the previous part, and enter it below:
y(t)=