I am working on the following series RLC circuit:
Let the circuit have non-zero initial conditions \$I(0^+)= 6\text{A}\$ and a voltage across the capacitor of \$V(0^+)=-12\text{V}\$.
What are \$\frac{dV(0^+)}{dt}\$ and \$\frac{dI(0^+)}{dt}\$?
My solution is different from the text example, and I want to know why.
$$I=\frac{dv}{dt} ~~\rightarrow ~~ \frac{dV(0^+)}{dt}=\frac{1}{C}I(0^+) = \frac{6}{C} $$
and
$$ v = L\frac{dI}{dt} ~~ \rightarrow ~~ \frac{dI(0^+)}{dt} = \frac{1}{L}V(0^+) =- \frac{12}{L}$$
The text, on the other hand, shows: $$\frac{dI(0^+)}{dt} = -\frac{1}{L}\Big[RI(0^+) + V(0^+)\Big]$$
What is going on here? What am I doing wrong?