e
Zoy
(a) y'' - y - 6y = 0; y? = e³?; y? = e?²?
(b) y'' - 25y = 0; y? = cosh 5t; y? = sinh 5t
t² + 2t
6. Show that y?(t) = is a solution of the nonhomogeneous linear ODE y' + 1/(t + 1)y = 2. Then find the general solution.
t + 1
7. Consider an RL electric circuit consisting of a resistor with resistance R (ohms) and an inductor with inductance L (henries)
connected in series with an impressed voltage (electromotive force) E(t) (volts). The differential equation governing the current,
I (amperes), in this circuit is derived using Kirchoff's Laws and is
dI
L ---- + RI = E(t)
dt
Suppose that R = 100 ohms, L = 2.5 henries and the constant impressed voltage is E(t) = E? = 110 volts. Time, t, is measured
in seconds.
