Determine the order and degree of the following differential equation: dydxdydxxdydxd2ydx2+dydx+x=1+d3ydx3 - Mathematics and Statistics

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Sum

Determine the order and degree of the following differential equation:

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

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Solution

The given D.E. is

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

On squaring both sides, we get

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

This D.E. has highest order derivative `("d"^3"y")/"dx"^3` with power 1.

∴ the given D.E. has order 3 and degree 1.

  Is there an error in this question or solution?
Chapter 6: Differential Equations - Exercise 6.1 [Page 193]

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