Mathematics

Problem

Which of the following best describes a first-order differential equation that allows the variables to be isolated on opposite sides of the equation? a) It can be rewritten in the form

\dfrac{dy}{dx}+P(x)y=Q(x)

, where

P

and

Q

involve only

x

. b) It can be rewritten in the form

g(y)\,\dfrac{dy}{dx}=f(x)

, where

f

involves only

x

and

g

involves only

y

. c) It can be rewritten in the form

\dfrac{dy}{dx}=f(x)+g(y)

, where

f

involves only

x

and

g

involves only

y

. d) It involves

y

but contains no explicit appearance of

x

on its right–hand side.

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