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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Determine the order and degree of the following differential equation: dydxdydx(d3ydx3)12-(dydx)13=20

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प्रश्न

Determine the order and degree of the following differential equation:

`(("d"^3"y")/"dx"^3)^(1/2) - ("dy"/"dx")^(1/3) = 20`

बेरीज
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उत्तर

`(("d"^3"y")/"dx"^3)^(1/2) - ("dy"/"dx")^(1/3) = 20`

`(("d"^3"y")/"dx"^3)^(1/2) = 20 + ("dy"/"dx")^(1/3)`

Taking power 6 on both sides.

`[(("d"^3"y")/"dx"^3)^(1/2)]^6 = [20 + ("dy"/"dx")^(1/3)]^6`

`(("d"^3"y")/"dx"^3)^3 = [20 + ("dy"/"dx")^(1/3)]^6`

∴ The given differential equation is radical and fraction free and its highest order is 3.

∴ Order = 3, degree = 3

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पाठ 6: Differential Equations - Exercise 6.1 [पृष्ठ १९३]

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बालभारती Mathematics and Statistics 2 (Arts and Science) [English] Standard 12 Maharashtra State Board
पाठ 6 Differential Equations
Exercise 6.1 | Q 9 | पृष्ठ १९३

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