Question

Determine order and degree (if defined) of differential equation: $(y"')^ 2 + (y")^3 + (y')^4 + y^5 = 0$

Answer 1

Answer:

Order=3

Degree=2

Solution:

Order of differential equation: Order is the highest numbered derivative in the equation.

Degree of differential equation: Degree is the highest power to which highest numbered derivative is raised when equation is free from radicals.

$(y"')^ 2 + (y")^3 + (y')^4 + y^5 = 0$
here highest numbered derivative is 3

So, order is 3

That highest number derivative raised to power 2,thus degree of differential equation is 2.

Hope it helps you.

Note:
${y}^{'} = \frac{dy}{dx} \\ \\ {y}^{''} = \frac{ {d}^{2}y }{ {dx}^{2} }$
and so on