Definition:Homogeneous Linear Second Order ODE

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A homogeneous linear second order ODE is a differential equation which is in (or can be manipulated into) the form:

$\dfrac {\mathrm d^2 y} {\mathrm d x^2} + P \left({x}\right) \dfrac {\mathrm d y} {\mathrm d x} + Q \left({x}\right) y = 0$

where, as is indicated by the notation, $P \left({x}\right)$ and $Q \left({x}\right)$ are functions of $x$ alone (or constants).

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