Question

If m and n are the order and degree of the differential equation `((d^3y)/(dx^3))^6+5((d^3y)/(dx^3))^4/((d^4y)/(dx^4))+(d^4y)/(dx^4)=x^3-1,` then ______.

Options

• m=4 and n = 5

• m = 4 and n = l

• m = 4 and n = 3

• m = 4 and n = 2

Answer 1

If m and n are the order and degree of the differential equation `((d^3y)/(dx^3))^6+5((d^3y)/(dx^3))^4/((d^4y)/(dx^4))+(d^4y)/(dx^4)=x^3-1,` then m = 4 and n = 2.

Explanation:

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

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

Here, the highest order derivative is `(d^4y)/(dx^4)` with power 2.

∴ order = 4 and degree = 2

∴ m=4 and n=2