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

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)

#### 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.

Concept: Order and Degree of a Differential Equation
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