Differential Equation Problem?

Note the equation is separable. DI / (V - IR) *(-R) = 1/L dt *(-R) log|V-IR| = -R/L*t + c So, |V - IR| = k*e^(-Rt/L). So, IR = V +- k*e^(-Rt/L).

Since, I(0) = 0. V +- k = 0 or 50 +- k = 0. Hence, IR = V - 50*e^(-Rt/L).

Now, solve for values by subbing in t = 0.5 s, L = 3 H, R = 10 ohms and V = 50 V.

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