Determine the order and degree of the following differential equation: yyxyy(y′′′)2+3y′′+3xy′+5y=0 - Mathematics and Statistics

Sum

Determine the order and degree of the following differential equation:

("y"''')^2 + 3"y"'' + 3"xy"' + 5"y" = 0

Solution

The given D.E. is

("y"''')^2 + 3"y"'' + 3"xy"' + 5"y" = 0

This can be written as:

(("d"^3"y")/"dx"^3)^2 + 3("d"^2"y")/"dx"^2 + "3x"("dy"/"dx") + 5"y" = 0

This D.E. has highest order derivative ("d"^3"y")/"dx"^3 with power 2.

∴ the given D.E. has order 3 and degree 2.

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