(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The equation [tex]\frac{dy}{dx}[/tex] = A(x)y^{2}+B(x)y+C(x) is called a Riccati equation. Suppose that one particular solution y_{1}(x) of this equation is known. Show that the substitution

y = y_{1}+[tex]\frac{1}{v}[/tex]

transforms the Riccati equation into the linear equation

[tex]\frac{dv}{dx}[/tex]+ (B+2Ay_{1})v = -A.

3. The attempt at a solution

So i know that y' = y_{1}' - [tex]\frac{v'}{v^2}[/tex] and I have tried substituting y and y' back into the original equation in order to simplify it down to the linear equation given. Unfortunately for some reason I am not getting anywhere. Any help would be appreciated!

Thanks,

Rob

P.S. Sorry for the crappy formatting, not really sure what I am doing.

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# Homework Help: Differential Equations homework problem.

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