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Friday, November 19, 2010

Watched MIT 18.03 - lecture 13

I watched another lecture on differential equations by Prof. Arthur Matuck.

Lecture 13 is about finding solutions to the following ODE:
$y'' + Ay' + By = e^{\alpha x}$, with $\alpha$ a complex number.

The general solution is
$y = C_1 y_1 + C_2 y_2 + \frac{e^{\alpha x}}
{\alpha^2 +A\alpha + B }$

$C_1 y_1 + C_2 y_2 = y_h$ is a solution the homogeneous part of the ODE and

$\frac{e^{\alpha x}}{\alpha^2 +A\alpha +B} = y_p$ is a particular solution of the ODE.

( I have not blogged about lectures 10,11 and 12 although I have seen them. Lectures 11 and 12 in particular were highly theoretical but did not add much in terms of new definitions or theorems.)

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