NCERT Solutions for Class 12 Maths<\/a> Chapter 9 Differential Equations Ex 9.1 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-9-ex-9-1\/<\/p>\nNCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Exercise 9.1<\/h2>\n <\/p>\n
Question 1. \n\\(\\frac { { d }^{ 4 }y }{ { dx }^{ 4 } } +({ sin }y^{ “‘ })\\) = 0 \nSolution: \nThe highest order derivatives is \\(\\frac { { d }^{ 4 }y }{ { dx }^{ 4 } }\\) \n\u2234 Order of the equation is 4 \nThe differential equation is not a polynomial equation in its derivatives. \nHence its degree is not defined.<\/p>\n
Question 2. \ny’ + 5y = 0 \nSolution: \nThe highest order derivative is y’ \n\u2234 Order is 1 \nThis is a polynomial equation in y’ and the \nHence its degree is 1.<\/p>\n
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Question 3. \n\\({ \\left( \\frac { ds }{ dt } \\right) }^{ 4 }+3s{ \\left( \\frac { { d }^{ 2 }s }{ { dt }^{ 2 } } \\right) }\\) = 0 \nSolution: \nThe highest order derivative is \\(\\frac{d^{2} s}{d t^{2}}\\) \n\u2234 Order is 2 \nThis is a polynomial equation in \\(\\frac{d^{2} s}{d t^{2}}\\) and \\(\\frac{ds}{dt}\\) and the power of \\(\\frac{d^{2} s}{d t^{2}}\\) is one \nHence its degree is one.<\/p>\n
Question 4. \n\\({ \\left( \\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \\right) }^{ 2 }+cos\\left( \\frac { dy }{ dx } \\right) =0\\) \nSolution: \nThe highest order derivatives is \\(\\frac{d^{2} y}{d x^{2}}\\) \n\u2234 Order of the equation is 2 \nThe differential equation is not a polynomial equation in its derivatives. \nHence its degree is not defined.<\/p>\n
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Question 5. \n\\(\\frac { { d }^{ 2 }y }{ { dx }^{ 2 } }\\) = cos3x + sin3x \nSolution: \nThe highest order derivative is \\(\\frac{d^{2} y}{d x^{2}}\\) \n\u2234 Order is 2 \nThis is a polynomial equation in \\(\\frac{d^{2} y}{d x^{2}}\\) and the power of \\(\\frac{d^{2} y}{d x^{2}}\\) is one \nHence its degree is one.<\/p>\n
Question 6. \n\\({ { (y }^{ ”’ }) }^{ 2 }+{ { ( }y^{ ” }) }^{ 3 }+{ { (y }^{ ‘ }) }^{ 4 }+{ y }^{ 5 }\\) = 0 \nSolution: \nThe highest order derivative is y”‘ \n\u2234 Order is 3 \nThis is a polynomial equation in y”‘, y” and y’ the power of y” is two. \nHence its degree is 2.<\/p>\n
Question 7. \ny”‘ + 2y” + y\u2019 = 0 \nSolution: \nThe highest order derivative is y”‘ \n\u2234 Order is 3 \nThis is a polynomial equation in y”‘, y” and y’ and the power of y”‘ is one. \nHence its degree is 1.<\/p>\n
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Question 8. \ny’ + y = ex<\/sup> \nSolution: \nThe highest order derivative is y’. \n\u2234 Order is 1 \nThis is a polynomial equation in y’ and the power of y’ is one. \nHence its degree is 1.<\/p>\nQuestion 9. \ny” + (y’) +2y = 0 \nSolution: \nThe highest order derivative is y” \n\u2234 Order is 2 \nThis is a polynomial equation in y” and \ny’ and the degree of y\u201d is one. \nHence its degree is 1.<\/p>\n
Question 10. \ny” + 2y’ + sin y = 0 \nSolution: \nThe highest order derivative is y”. \n\u2234 Order is 2 \nThis is a polynomial equation in y”, y’ and the power of y” is one. \nHence its degree is 1.<\/p>\n
Question 11. \nThe degree of the differential equation \n\\({ \\left( \\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \\right) }^{ 3 }{ +\\left( \\frac { dy }{ dx } \\right) }^{ 2 }+sin{ \\left( \\frac { dy }{ dx } \\right) }+1=0\\) \n(a) 3 \n(b) 2 \n(c) 1 \n(d) not defined \nSolution: \nThe differential equation is not a polynomial equation in derivatives. Hence the degree is not defined.<\/p>\n
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Question 12. \nThe order of the differential equation \n\\({ 2x }^{ 2 }\\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } -3\\frac { dy }{ dx } +y=0\\) \n(a) 2 \n(b) 1 \n(c) 0 \n(d) not defined \nSolution: \nThe highest order derivative is \\(\\frac{d^{2} y}{d x^{2}}\\) \n\u2234 Order is 2.<\/p>\n","protected":false},"excerpt":{"rendered":"
These NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.1 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-9-ex-9-1\/ NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Exercise 9.1 Question 1. = 0 Solution: The highest order derivatives is \u2234 Order of the equation is 4 The …<\/p>\n
NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.1<\/span> Read More »<\/a><\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","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":"default","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","spay_email":""},"categories":[3],"tags":[],"yoast_head":"\nNCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.1 - MCQ Questions<\/title>\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\t \n\t \n\t \n