The circuit above has a resistor, inductor and voltage source. The resistance is $\displaystyle {R}={35}$ Ohms, the inductance is $\displaystyle {L}={3}$ Henrys and the voltage source has voltage $\displaystyle {V}{\left({t}\right)}={285}{\cos{{\left({5}{t}\right)}}}$ after $\displaystyle {t}$ seconds.

a) Let $\displaystyle {i}{\left({t}\right)}$ be the current (in Amperes) in the circuit after $\displaystyle {t}$ seconds and find a differential equation for $\displaystyle {i}'{\left({t}\right)}$.

$\displaystyle {i}'{\left({t}\right)}=$ Preview Question 6 Part 1 of 3   .

b) Now assume the initial condition $\displaystyle {i}{\left({0}\right)}={0}$ A. Find the current after 0.3 seconds.

$\displaystyle {i}{\left({0.3}\right)}=$ Preview Question 6 Part 2 of 3  

c) Using a step size of 0.03 and the Improved Euler (Heun's) Method, approximate the current in the circuit after 0.3 seconds using the model from part (b).

$\displaystyle {i}{\left({0.3}\right)}\approx$