# Thread: linearizing a 2nd order ODE

1. ## 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

2. Originally Posted by carnot
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

$
P Q \frac{dQ}{dP} + Q^2 + bP(1-P) = 0
$
(Bernoulli)

and further letting $R = Q^2$ gives

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