Answer:
We can solve this first-order linear ordinary differential equation using separation of variables.
Starting with the given equation:
10^-2 dv(t)/dt + v(t) = 0
We can rearrange it as:
dv(t)/dt = -10^2 v(t)
Now, separate the variables by dividing both sides by v(t) and dt:
1/v(t) dv(t) = -10^2 dt
Integrate both sides with respect to their respective variables:
∫ 1/v(t) dv(t) = ∫ -10^2 dt
ln|v(t)| = -10^2 t + C
where C is the constant of integration.
Solving for v(t), we exponentiate both sides:
|v(t)| = e^-10^2t * e^C
Using the initial condition v(0) = 100 V, we can determine the value of the constant of integration:
|v(0)| = e^C
100 = e^C
C = ln 100
Therefore, the general solution for v(t) is:
v(t) = ± 100 e^-10^2t
However, since v(0) = 100 V is positive, the solution we want is:
v(t) = 100 e^-10^2t
This is the function that satisfies the given differential equation and initial condition.