How do you solve a differential equation with a delta function?

Question

I was solving for an electrical circuit and wound up with this equation: $10di/dt +10i -24\delta(t) = 0$

How do you solve this? Laplace transform?

Answer 1

With the integrating factor $e^t$ for $i'(t)+i(t)$ you get $$ (e^ti(t))'=2.4·e^t·δ(t)=2.4·δ(t) $$ as $e^0=1$. Thus $$ e^ti(t)-i(0)=2.4·H(t)\iff i(t)=(i(0)+2.4·H(t))·e^{-t} $$