Differential Equations — Important Questions

1

The derivative \( \frac{dy}{dx} \) is of degree 1 as it is not raised to any power.

\( \frac{dy}{dx} = 2x \)

A differential equation involves derivatives. \( \frac{dy}{dx} = 2x \) contains a derivative and is a differential equation.

\( y = \int f(x) dx + c \)

Integrating both sides of \( \frac{dy}{dx} = f(x) \) gives \( y = \int f(x) dx + c \), where c is an arbitrary constant.

Linear, Homogeneous, First order

The equation can be written as \( \frac{dy}{dx} = -\frac{x}{y} \). It is linear in terms of differentials, homogeneous (both terms degree 1), and first order.