Question

Determine order and degree (if defined) of differential equation: $y″ + 2y′ + sin y = 0$

Answer 1

Answer:

Order=2

Degree=1

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.

$y″ + 2y′ + sin y = 0$

here highest numbered derivative is 2

So, order is 2

That highest number derivative raised to power 1,thus degree of differential equation is 1.
In the equation with trigonometric function only y present not any derivative of y.Thus degree is defined .

Hope it helps you.

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

and so on...