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3 years ago

8

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example tha

t disproves the statement.
The equation y' = 3y - 2x + 6xy - 1 is separable.

1 answer:

ioda3 years ago

3 0

True.

You're allowed to move stuff around. Dogs of the AMS.

$y' = 3y - 2x + 6xy - 1 \\
y' = 3y + 6xy - 2x - 1 \\
dy/dx= 3y(1 + 2x) - (2x + 1) \\
dy/dx = 3y(1 + 2x) - (1 + 2x) \\
\frac{dy}{dx} = (3y - 1)(1 + 2x) \ \Rightarrow\ \dfrac{dy}{3y-1} = (1 + 2x) dx$

We wrote it in the form dy/dx = g(x) f(y) so this is separable.

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