Question

5. (a) An RL circuit is governed by the equation: dI/dt + 20 I = 100, t > 0, where I is the current. Solve this equation if I = 4 at t = 0. Find the steady-state current. How long does it take for the current to achieve the value I = 4.5? [5 marks] (b) Solve the following initial value problem for a function x = x(t): d^2x/dt^2 - 6dx/dt + 10x = 0, t > 0, subject to x(0) = 1, dx/dt(0) = 0. [5 marks] 6. Find the general solution of each of the following nonhomogeneous differential equations: (i) d^2x/dt^2 + 9x = cos t [5 marks] (ii) d^2x/dt^2 + dx/dt - 2x = 3 e^t [5 marks]

          5. (a) An RL circuit is governed by the equation:
dI/dt + 20 I = 100, t > 0,
where I is the current. Solve this equation if I = 4 at t = 0. Find the steady-state current.
How long does it take for the current to achieve the value I = 4.5? [5 marks]
(b) Solve the following initial value problem for a function x = x(t):
d^2x/dt^2 - 6dx/dt + 10x = 0, t > 0,
subject to
x(0) = 1, dx/dt(0) = 0.
[5 marks]
6. Find the general solution of each of the following nonhomogeneous differential equations:
(i) d^2x/dt^2 + 9x = cos t [5 marks]
(ii) d^2x/dt^2 + dx/dt - 2x = 3 e^t [5 marks]

5. (a) An RL circuit is governed by the equation:
dI/dt + 20 I = 100, t > 0,
where I is the current. Solve this equation if I = 4 at t = 0. Find the steady-state current.
How long does it take for the current to achieve the value I = 4.5? [5 marks]
(b) Solve the following initial value problem for a function x = x(t):
d^2x/dt^2 - 6dx/dt + 10x = 0, t > 0,
subject to
x(0) = 1, dx/dt(0) = 0.
[5 marks]
6. Find the general solution of each of the following nonhomogeneous differential equations:
(i) d^2x/dt^2 + 9x = cos t [5 marks]
(ii) d^2x/dt^2 + dx/dt - 2x = 3 e^t [5 marks]

Added by Julie M.

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