Question

Determine the order and degree of the given differential equation: $e^{\frac{dy}{dx}}+\frac{dy}{dx}=x$

Answer 1

➡️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

$e^{\frac{dy}{dx}}+\frac{dy}{dx}=x$

here highest derivative is :1

As we know that $\frac{dy}{dx}$

ie Order is 1.

and the complete equation is free from radicals, but first derivative comes with exponent i.e. e^(dy/dx), thus the given differential equation is not applicable to calculate degree .

So, Degree = None.