Question

Determine the order and degree of the given differential equation: $\frac{d^{4}y}{dx^{4}}=[1+(\frac{dy}{dx})^{2}]^{3}$

Answer 1

Solution:
➖➖➖

➡️Order of a DE: Order is calculated by checking higher order derivative of x. All DE have order.

➡️Degree of DE: Degree is the power of highest order derivative,when complete equation is free from radicals. Every differential equation does not have degree.

Here in the give DE

$\frac{d^{4}y}{dx^{4}}=[1+(\frac{dy}{dx})^{2}]^{3}$

here highest derivative is :4

$\frac{d^{4}x}{dt^{4}}$

ie Order is 4.

and the complete equation is free from radicals, thus power of forth derivative is degree of it.

So, Degree = 1