- #1
Moridin
- 692
- 3
Homework Statement
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)
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) ?