Choose the correct answer.
(1) A first order differential equation of the form y′ = f(x) is called ········· variable.
  (A) Non-separable (B) Linear (2) If f(x)dy = g(y)dx, then
(C) Exact
(D) Separable

Let's break down both parts of the question:

### (1) "A first-order differential equation of the form \( y' = f(x) \) is called..."
- This equation has the form \( \frac{dy}{dx} = f(x) \), which does **not involve the variable \( y \)** on the right-hand side. This is a simple form of a **linear differential equation**. In this case, it's called **Linear** because it's of the form \( y' = f(x) \), where the derivative of \( y \) is a function of \( x \) only and doesn't involve nonlinear terms.

Thus, the correct answer for (1) is:
**(B) Linear**

### (2) "If \( f(x)dy = g(y)dx \), then the differential equation is..."
- This equation can be rewritten as:
  \[
  \frac{dy}{g(y)} = \frac{dx}{f(x)}
  \]
  which is a **separable** differential equation because the variables \( x \) and \( y \) can be separated on opposite sides of

Choose the correct answer.
(1) A first-order differential equation of the form y′ = f(x) is called ········· variable.
  (A) Non-separable (B) Linear
(2) If f(x)dy = g(y)dx, then
(C) Exact
(D) Separable

Explore how to solve first-order differential equations, including linear equations of the form y' = f(x) and separable equations f(x)dy = g(y)dx. This guide provides step-by-step explanations suitable for undergraduate mathematics students.

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