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Math Help - linearizing a 2nd order ODE

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    linearizing a 2nd order ODE

    what is the linearized form of the following and what is the method to get a linearized form?:

    P*d^2P/dz^2 + (dP/dz)^2 +b*P(1-P) = 0

    b=constant
    P'(0)=0
    P(1)=0.1
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  2. #2
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    Quote Originally Posted by carnot View Post
    what is the linearized form of the following and what is the method to get a linearized form?:

    P*d^2P/dz^2 + (dP/dz)^2 +b*P(1-P) = 0

    b=constant
    P'(0)=0
    P(1)=0.1
    If you let Q = \frac{dP}{dz} then your ODE becomes

     <br />
P Q \frac{dQ}{dP} + Q^2 + bP(1-P) = 0<br />
(Bernoulli)

    and further letting R = Q^2 gives

     <br />
P \frac{dR}{dP} + 2 R + 2bP(1-P) = 0<br />
a linear ODE!
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