A differential equation that contains derivative of a function with an exponent one is called the differential equation of the first order and first degree.

In calculus, we see several types of differential equations but the first order and first degree differential equations are frequently appeared. So, let us learn how the differential equations of first order and first degree look like.

$(x^2-yx^2)\dfrac{dy}{dx}$ $+$ $y^2$ $+$ $xy^2$ $\,=\,$ $0$

In this example, $x$ and $y$ are variables but $y$ represents a function in terms of $x$. The function $y$ is differentiated one time and there is no other derivatives in the given differential equation. Hence, it is called the first order differential equation.

$\implies$ $(x^2-yx^2)\Bigg(\dfrac{dy}{dx}\Bigg)^1$ $+$ $y^2$ $+$ $xy^2$ $\,=\,$ $0$

The power of the derivative of the function is one. Hence, it is a first degree differential equation.

Therefore, the given differential equation is called the differential equation of first order and first degree.

The following are some more examples for the first order and first degree differential equations.

$(1)\,\,\,$ $\sec^2{y}\tan{x}\dfrac{dy}{dx}$ $+$ $\sec^2{x}\tan{y} = 0$

$(2)\,\,\,$ $(x-y)^2\dfrac{dy}{dx} = a^2$

$(3)\,\,\,$ $\dfrac{dy}{dx} = -\dfrac{x\sqrt{1-y^2}}{y\sqrt{1-x^2}}$

$(4)\,\,\,$ $\dfrac{dy}{dx}$ $\,=\,$ $e^{2x-3y}+4x^2e^{-3y}$

$(5)\,\,\,$ $x^4\dfrac{dy}{dx}$ $+$ $x^3y$ $+$ $\log_e{(xy)}$ $\,=\,$ $0$

Latest Math Topics

Jul 24, 2022

Jul 15, 2022

Latest Math Problems

Jul 29, 2022

Jul 17, 2022

Jun 02, 2022

Apr 06, 2022

A best free mathematics education website for students, teachers and researchers.

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Learn how to solve the maths problems in different methods with understandable steps.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved