Which of the following best describes a first-order differential equation that allows…

MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations

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.

Related theory

Separation of Variables
Solutions
Variable separable equations
Differential equations with variables separable
Differential Equations

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