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

I'm having trouble understanding my class notes from a lecture on separable differential equations.

I would like to solve the equation g(y)y' = f(x)

3. The attempt at a solution

g(y)y' = f(x), G(x), F(x) exists and are continuous

The left side is the derivative of G(y(x)) and the right is F(x) + C

[tex]\frac{d}{dx} G(y(x)) = \frac{d}{dx} F(x) + C[/tex]

G'(y(x))y'(x) = g(y(x))y'(x)

[tex]\frac{d}{dx} (F(x) + C) = F'(x) + 0 = f(x)[/tex]

G(y(x)) = F(x) + C

So do you simply do

G^{-1}(G(y(x))) = y(x) = G^{-1}(F(x)) + G^{-1}(C) ?

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# Homework Help: Separable Differential Equations

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