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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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 $\displaystyle Q = \frac{dP}{dz}$ then your ODE becomes $\displaystyle P Q \frac{dQ}{dP} + Q^2 + bP(1-P) = 0 $ (Bernoulli) and further letting $\displaystyle R = Q^2$ gives $\displaystyle P \frac{dR}{dP} + 2 R + 2bP(1-P) = 0 $ a linear ODE!
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