Determine the order and degree of the differential equation d y d x 4 + y 5 = d 3 y d x 3

The given differential equation is d y d x 4 + y 5 = d 3 y d x 3 . The highest order derivative present in this equation is d 3 y d x 3 and its power is 1 . So, the given differential equation is of 3 order and degree 1 .

Determine the order and degree of the differential equation d y d x 4 + y 5 = d 3 y d x 3

The given differential equation is d y d x 4 + y 5 = d 3 y d x 3 . The highest order derivative present in this equation is d 3 y d x 3 and its power is 1 . So, the given differential equation is of 3 order and degree 1 .

Determine the order and degree of the differential equation a d 2 y d x 2 = 1 + d y d x 2 3 2

The given differential equation is a d 2 y d x 2 = 1 + d y d x 2 3 2 ⇒ a d 2 y d x 2 2 = 1 + d y d x 2 3 The highest order derivative present in this equation is d 2 y d x 2 and its power is 2 . So, it is a non-linear differential equation with order 2 and degree 2 .

Determine the order and degree of the differential equation d y d t y + d y d t = y t d y d t

The given differential equation is d y d t y + d y d t = y t d y d t ⇒ d y d t d y d t = y t y + d y d t ⇒ d y d t 2 = t y 2 + y t × d y d t Now, the highest order derivative present in this equation is d y d t and its power is 2 . So, the given differential equation is of degree 2 and order 1 .

Determine the order and degree of the differential equation d 2 y d u 2 = 3 y + d y d u d 2 y d u 2

The given differential equation is d 2 y d u 2 = 3 y + d y d u d 2 y d u 2 ⇒ d 2 y d u 2 d 2 y d u 2 = 3 y + d y d u ⇒ d 2 y d u 2 1 + 1 2 = 3 y + d y d u ⇒ d 2 y d u 2 3 2 = 3 y + d y d u ⇒ d 2 y d u 2 3 = 3 y + d y d u 2 Now, the highest order derivative present in this equation is d 2 y d u 2 and its power is 3 . So, the given differential equation is of degree 3 and order 2 .