Question

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

Answer 1

Order is the highest no of derivative. Hence order is 2. (D2y/dx2)

Degree is the power of that highest derivative. (D2y/dx2)2

Hence power is 2

Answer 2

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

$(\frac{d^{2}y}{dx^{2}})^{2}+(\frac{dy}{dx})^{3}=e^{x}$

here highest derivative is :2

$\frac{ {d}^{2}y }{ {dx}^{2} }$
ie Order is 2.

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

Degree = 2