The current $I$ in an electric circuit at time $t$ satisfies the differential equation \[4\frac{

Question

The current $I$ in an electric circuit at time $t$ satisfies the differential equation $$4\frac{\mathrm{d}I}{\mathrm{d}t}=2-3I.$$ Find $I$ in terms of $t$, given that $I=2$ when $t=0$. State what happens to the current in this circuit for large values of $t$.

Accepted Answer

(a) $I=\frac23(1+2e^{-\frac34t})$. (b) $I\to\frac23$ as$t\to\infty$, decreasing from 2.

Differential Equations - Equilibrium Solutions and Long-Term Behaviour

Differential Equations - Equilibrium Solutions and Long-Term Behaviour

Solution:

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