{"id":5698,"date":"2021-09-29T18:35:44","date_gmt":"2021-09-29T13:05:44","guid":{"rendered":"https:\/\/mathemerize.com\/?p=5698"},"modified":"2021-11-21T20:17:22","modified_gmt":"2021-11-21T14:47:22","slug":"degree-and-order-of-differential-equation","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/degree-and-order-of-differential-equation\/","title":{"rendered":"Degree and Order of Differential Equation"},"content":{"rendered":"

Here you will learn what is differential equation and degree and order of differential equation with examples.<\/p>\n

Let’s begin –<\/p>\n

Differential Equation<\/h2>\n

An equation containing an independent variable, dependent variable and differential coefficients of dependent variable with respect to independent variable is called a differential equation.<\/p>\n

for example<\/strong> : \\(dy\\over dx\\) = 2xy and \\(d^2y\\over dx^2\\) = 4x are examples of differential equations.<\/p>\n

Degree and Order of Differential Equation<\/h2>\n

Order of Differential Equation<\/strong><\/h4>\n
\n

The order of a differential equation is the order of the highest order derivative appearing in the equation.<\/p>\n<\/blockquote>\n

Example 1<\/strong><\/span> : In the equation \\(d^2y\\over dx^2\\) + 3\\(dy\\over dx\\) + 2y = \\(e^x\\), the order of highest order derivative is 2. So, it is a differential equation of order 2.<\/p>\n

Example 2<\/span><\/strong> : In the equation \\(d^3y\\over dx^3\\) – 6\\(({dy\\over dx})^2\\) – 4y = 0, the order of highest order derivative is 3. So, it is a differential equation of order 3.<\/p>\n

Degree of Differential Equation<\/strong><\/h4>\n
\n

The degree of a differential equation is the degree of the highest order derivative, when differential coefficients are made free from radicals and fractions.<\/p>\n<\/blockquote>\n

Example 1<\/strong><\/span> : In the equation \\(d^3y\\over dx^3\\) – 6\\(({dy\\over dx})^2\\) – 4y = 0, the power of highest order derivative is 1. So, it is a differential equation of degree 1.<\/p>\n

Example 2<\/span><\/strong> : Consider the differential equation x\\(({d^3y\\over dx^3})^2\\) – 6\\(({dy\\over dx})^4\\) + \\(y^4\\) = 0.<\/p>\n

Solution<\/span><\/strong> : In this equation, the order of the highest order derivative is 3 and its power is 2. So, it is a differential equation of order 3 and degree 2.<\/p>\n

Example 3<\/span><\/strong> : Consider the differential equation \\(({1 + ({dy\\over dx})^2})^{3\/2}\\) = k\\({d^2y\\over dx^2}\\).<\/p>\n

Solution<\/span><\/strong> : The order of highest order differential coefficient is 2. So, its order is 2.<\/p>\n

To find its degree we express the differential equation as a polynomial in derivatives. When expressed as a polynomial in derivatives it becomes \\(k^2\\)\\(({d^2y\\over dx^2})^2\\) – \\(({1 + ({dy\\over dx})^2})^3\\) = 0. Clearly, the power of the highest order differential coefficient is 2. So, its degree is 2.<\/p>\n\n\n

\n
Next – Formation of Differential Equation<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn what is differential equation and degree and order of differential equation with examples. Let’s begin – Differential Equation An equation containing an independent variable, dependent variable and differential coefficients of dependent variable with respect to independent variable is called a differential equation. for example : \\(dy\\over dx\\) = 2xy and \\(d^2y\\over …<\/p>\n

Degree and Order of Differential Equation<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[38],"tags":[263,265,251,264],"yoast_head":"\nDegree and Order of Differential Equation - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is differential equation and degree and order of differential equation with examples.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/degree-and-order-of-differential-equation\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Degree and Order of Differential Equation - 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