The degree of the differential equation d^4y/dx^4 + (d^3y/dx^3)^8 + (d^2y/dx^2)^6 + 8y = 5x isa) 1 b) 8 c) 6 d) 4 d^4y/dx^4 + (d^3y/dx^3)^8 + (d^2y/dx^2)^6 + 8y = 5x 

Expert Answers
lemjay eNotes educator| Certified Educator

In differential equation, degree is the exponent of the order of differential equation.

And order of differential equation refers to the highest derivative.

For example:

`((d^2y)/(dx^2))^4 - (dy)/(dx) = 0`

>The equation is of order 2 or second order, since `(d^2y)/(dx^2)` is the highest derivative.

> Since the highest derivative is raised to a power of 4 `(((d^2y)/(dx^2))^4)` ,the degree of the differential equation is 4.

As for the problem above, we may re-write it as:

`((d^4y)/(dx^4))^1+((d^3y)/(dx^3))^8 +((d^2y)/(dx^2))^6+8y=5x`

since` (d^4y)/(dx^4)` is the same as `((d^4y)/(dx^4))^1` . 

The highest derivative present in the equation is `(d^4y)/(dx^4)` and it is raised to a power of 1.

Hence, the degree of the given differential equation is 1 .