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Math Help - Derivative Question...

  1. #1
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    Derivative Question...

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    Quote Originally Posted by qbkr21 View Post
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    start with y = e^{rx} find y', and y'' then plug them into your equation. when it's all said and done, you should end up with a quadratic in r, just solve it
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    Re:

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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by qbkr21 View Post
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    e^{rx} is never zero no matter what r is (as long as r \in \mathbb {R}). remember what the graph looks like
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    is up to his old tricks again! Jhevon's Avatar
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    i don't know if you are doing or will do differential equations, but what you are doing here is in fact the general method for solving second order differential equations with constant coefficients.

    so in general, when given a homogeneous (which just means equated to zero) differential equation of the form:
    ay'' + by' + cy = 0

    we assume a solution y = e^{rx}, and then obtain the "characteristic equation":

    ar^2 + br + c = 0 ..........(1)

    differential equation students usually jump to equation (1) after the first line and then continue
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