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Thread: How to solve the following ODE using method of undetermined coefficients

  1. #1
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    How to solve the following ODE using method of undetermined coefficients

    q'' + 4q' +3q
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  2. #2
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    Re: How to solve the following ODE using method of undetermined coefficients

    the method of undetermined coefficients is used when you have a driving function.

    If you just want the homogeneous solution the method doesn't enter into it.

    Just find the roots $r_1, r_2$ of the characteristic equation

    $s^2 + 4s + 3=0$

    and the solutions will be

    $q(x) = c_1 e^{r_1 x} + c_2 e^{r_2 x},~c_1, c_2 \in \mathbb{C}$

    In this case

    $(s+3)(s+1)=0$

    $r_1 = -3,~r_2 = -1$

    $q(x) = c_1 e^{-3x}+c_2 e^{-x}, c_2 \in \mathbb{C}$
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