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I have the following differential equation with an impulse described by the Dirac delta function

dx/dt (t) = - a⋅x(t) + d⋅delta(t) x(0)=0

with a,d scalars. My problem is this delta function in the right hand side.

Is there an equivalent formulation without the delta function, e.g. putting the d into the initial value?

How could I solve this numerically, e.g. in Matlab?

Many thanks for any suggestions.