In Exercise, use a numerical solver to sketch the solution of the given initial value prob...

In Exercise, use a numerical solver to sketch the solution of the given initial value problem.

(i) Where does your solver experience difficulty? Why? Use the image of your solution to estimate the interval of existence.

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(ii) For 11–14 only, find an explicit solution; then use your formula to determine the interval of existence. How does it compare with the approximation found in part (i)?

,y(0) = 3

An electric circuit, consisting of a capacitor, resistor, and an electromotive force can be modeled by the differential equation

where R and C are constants (resistance and capacitance) and q = q(t) is the amount of charge on the capacitor at time t. For simplicity in the following analysis, let R = C = 1, forming the differential equation dq/dt + q = E(t).