Question

QUESTION THREE 3 Consider the third order ordinary differential equation \frac{d^3x}{dt^3} - 2\frac{d^2x}{dt^2} - \frac{dx}{dt} + 2x = 0, where $x(0) = 0$, $\frac{dx}{dt}(0) = 1$ and $\frac{d^2x}{dt^2}(0) = 1$. (a) Convert the ordinary differential equation into a system of three first order linear ordinary differential equation. [5 Marks] (b) Write the system of equations in the vector-matrix form $\frac{dx}{dt} = Ax$. [5 Marks] (c) Use the fundamental matrix solution technique to solve the system of ordinary differential equation. [15 Marks] (d) Hence write down a solution to the original third order equation. [5 Marks]

          QUESTION THREE
3
Consider the third order ordinary differential equation
\frac{d^3x}{dt^3} - 2\frac{d^2x}{dt^2} - \frac{dx}{dt} + 2x = 0,
where $x(0) = 0$, $\frac{dx}{dt}(0) = 1$ and $\frac{d^2x}{dt^2}(0) = 1$.
(a) Convert the ordinary differential equation into a system of three first order linear
ordinary differential equation.
[5 Marks]
(b) Write the system of equations in the vector-matrix form
$\frac{dx}{dt} = Ax$.
[5 Marks]
(c) Use the fundamental matrix solution technique to solve the system of
ordinary differential equation.
[15 Marks]
(d) Hence write down a solution to the original third order equation.
[5 Marks]

QUESTION THREE
3
Consider the third order ordinary differential equation
(d^3x)/(dt^3) - 2(d^2x)/(dt^2) - (dx)/(dt) + 2x = 0,
where x(0) = 0, (dx)/(dt)(0) = 1 and (d^2x)/(dt^2)(0) = 1.
(a) Convert the ordinary differential equation into a system of three first order linear
ordinary differential equation.
[5 Marks]
(b) Write the system of equations in the vector-matrix form
(dx)/(dt) = Ax.
[5 Marks]
(c) Use the fundamental matrix solution technique to solve the system of
ordinary differential equation.
[15 Marks]
(d) Hence write down a solution to the original third order equation.
[5 Marks]

Added by Daniel C.

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