{"id":28218,"date":"2024-10-22T11:49:02","date_gmt":"2024-10-22T06:19:02","guid":{"rendered":"https:\/\/samacheerkalvi.guide\/?p=28218"},"modified":"2024-10-23T10:04:39","modified_gmt":"2024-10-23T04:34:39","slug":"samacheer-kalvi-12th-maths-guide-chapter-10-ex-10-1","status":"publish","type":"post","link":"https:\/\/samacheerkalvi.guide\/samacheer-kalvi-12th-maths-guide-chapter-10-ex-10-1\/","title":{"rendered":"Samacheer Kalvi 12th Maths Guide Chapter 10 Ordinary Differential Equations Ex 10.1"},"content":{"rendered":"

Tamilnadu State Board New Syllabus\u00a0Samacheer Kalvi 12th Maths Guide<\/a> Pdf Chapter 10 Ordinary Differential Equations Ex 10.1 Textbook Questions and Answers, Notes.<\/p>\n

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 10 Ordinary Differential Equations Ex 10.1<\/h2>\n

Question 1.
\nFor each of the following equations, determine its order, degree (if exists)
\n(i) \\(\\frac { dy }{ dx }\\) + xy = cot x
\n(ii) (\\(\\frac { d^3y }{ dx^3 }\\))2\/3<\/sup> – 3 \\(\\frac { d^2y }{ dx^2 }\\) + 5\\(\\frac { dy }{ dx }\\) + 4 = 0
\n(iii) (\\(\\frac { d^2y }{ dx^2 }\\))2<\/sup> + (\\(\\frac { dy }{ dx }\\))\u00b2 = x sin (\\(\\frac { d^2y }{ dx^2 }\\))
\n(iv) \\(\\sqrt{\\frac { dy }{ dx }}\\) – 4 \\(\\frac { dy }{ dx }\\) – 7x = 0
\n(v) y(\\(\\frac { dy }{ dx }\\)) = \\(\\frac { x }{ (\\frac { dy }{ dx })+(\\frac { dy }{ dx })^3 }\\)
\n(vi) x\u00b2\\(\\frac { d^2y }{ dx^2 }\\) + [1 + (\\(\\frac { dy }{ dx }\\))\u00b2]1\/2<\/sup> = 0
\n(vii) (\\(\\frac { d^2y }{ dx^2 }\\))\u00b3 = \\(\\sqrt{1+(\\frac { dy }{ dx })}\\)
\n(viii) \\(\\frac { d^2y }{ dx^2 }\\) = xy + cos (\\(\\frac { dy }{ dx }\\))
\n(ix) \\(\\frac { d^2y }{ dx^2 }\\) + 5 \\(\\frac { dy }{ dx }\\) + \u222b ydx = x\u00b3
\n(x) x = exy(\\(\\frac { dy }{ dx }\\))<\/sup>
\nSolution:
\n(i) \\(\\frac { dy }{ dx }\\) + xy = cot x
\nIn the given equation, the highest order derivative is \\(\\frac { dy }{ dx }\\) only its power is 1
\n\u2234 Its order = 1 & degree = 1<\/p>\n

\"Samacheer<\/p>\n

(ii) (\\(\\frac { d^3y }{ dx^3 }\\))2\/3<\/sup> – 3 \\(\\frac { d^2y }{ dx^2 }\\) + 5\\(\\frac { dy }{ dx }\\) + 4 = 0
\nTaking power 3 on both sides, we get
\n(\\(\\frac { d^3y }{ dx^3 }\\))2<\/sup> = (3 \\(\\frac { d^2y }{ dx^2 }\\) – 5\\(\\frac { dy }{ dx }\\) – 4)\u00b3
\nIn the equation (1), the highest order derivative is \\(\\frac { d^3y }{ dx^3 }\\) and its power is 2.
\n\u2234 Its order = 3 & degree = 2<\/p>\n

(iii) (\\(\\frac { d^2y }{ dx^2 }\\))2<\/sup> + (\\(\\frac { dy }{ dx }\\))\u00b2 = x sin (\\(\\frac { d^2y }{ dx^2 }\\))
\nIn the equation, the highest order derivative is \\(\\frac { d^2y }{ dx^2 }\\) and its order is 2.
\nIt has a term sin (\\(\\frac { d^2y }{ dx^2 }\\)), so its degree is not defined or degree does not exist.<\/p>\n

\"Samacheer<\/p>\n

\"Samacheer
\non squaring both sides,
\n\\(\\frac { dy }{ dx }\\) = 16 (\\(\\frac { dy }{ dx }\\))\u00b2 + 49 x\u00b2 + 56x \\(\\frac { dy }{ dx }\\)
\nclearly, it is a differential equation of order = 1 & degree = 2.<\/p>\n

\"Samacheer
\nIn this equation, the highest order derivative is \\(\\frac { dy }{ dx }\\) & its power is 4.
\n\u2234 Its order = 1 & degree = 4<\/p>\n

\"Samacheer<\/p>\n

\"Samacheer
\nIn this equation, the highest order derivative is \\(\\frac { d^2y }{ dx^2 }\\) & its power is 2.
\n\u2234 Its order = 2 & degree = 2<\/p>\n

\"Samacheer
\nIn this equation, the highest order derivative is \\(\\frac { d^2y }{ dx^2 }\\) & its power is 6.
\n\u2234 Its order = 2 & degree = 6<\/p>\n

\"Samacheer<\/p>\n

(viii) \\(\\frac { d^2y }{ dx^2 }\\) = xy + cos (\\(\\frac { dy }{ dx }\\))
\nIn this equation, the highest order derivative is \\(\\frac { d^2y }{ dx^2 }\\) & its power is 2.
\nIt has a term cos(\\(\\frac { dy }{ dx }\\)), so its degree is not defined or degree does not exist.<\/p>\n

(ix) \\(\\frac { d^2y }{ dx^2 }\\) + 5 \\(\\frac { dy }{ dx }\\) + \u222b ydx = x\u00b3
\ndifferentiating with respect to x, we get
\n\\(\\frac { d^3y }{ dx^3 }\\) + 5 \\(\\frac { d^2y }{ dx^2 }\\) + y = 3x\u00b2
\nIn this equation the highest order derivative is \\(\\frac { d^3y }{ dx^3 }\\) & its power is 1
\n\u2234 Its order = 3 & degree = 1<\/p>\n

(x) x = exy(\\(\\frac { dy }{ dx }\\))<\/sup>
\nIn this equation the highest order derivative is \\(\\frac { dy }{ dx }\\) & its order is 1
\nIt has the term exy(\\(\\frac { dy }{ dx }\\))<\/sup>
\nSo its degree is not defined or degree does not exist.<\/p>\n

\"Samacheer<\/p>\n","protected":false},"excerpt":{"rendered":"

Tamilnadu State Board New Syllabus\u00a0Samacheer Kalvi 12th Maths Guide Pdf Chapter 10 Ordinary Differential Equations Ex 10.1 Textbook Questions and Answers, Notes. Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 10 Ordinary Differential Equations Ex 10.1 Question 1. For each of the following equations, determine its order, degree (if exists) (i) + xy = cot x …<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[5],"tags":[],"class_list":["post-28218","post","type-post","status-publish","format-standard","hentry","category-class-12"],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts\/28218"}],"collection":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/comments?post=28218"}],"version-history":[{"count":1,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts\/28218\/revisions"}],"predecessor-version":[{"id":41411,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts\/28218\/revisions\/41411"}],"wp:attachment":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/media?parent=28218"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/categories?post=28218"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/tags?post=28218"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}