The value of the resistor is R=8Ω. Assume that at the instant the 2 A dc current source is applied to the circuit, the initial current in the 25 mH inductor is 1 A, and the initial voltage on the capacitor is 50 V (positive at the upper terminal).

a. Find the derivative of the inductor current iL(t) at time t=0+
b. Find the differential equation satisfied by the inductor current, iL(t) for t>0 . Write the differential equation in the form ad2iL/dt2+bdiL/dt+iL(t)=c , where a, b,c are constants. Find the values of a, b,c .
c. Find the roots of the characteristic equation associated with the differential equation you found in Part B. Enter the roots s1,s2 in units of rad/sec separated by a comma. For real roots, enter the smallest root first. For complex roots, enter the root with the positive imaginary part first.
d. Find iL(t) for t≥0.