Write down, showing reasons, the order and degree of d 2 x d t 2 − x + d x d t 2 4 = 0 .

Given differential equation d 2 x d t 2 − x + d x d t 2 4 = 0 ⇒ d 2 x d t 2 = x + d x d t 2 4 ⇒ d 2 x d t 2 4 = x + d x d t 2 4 4 ⇒ d 2 x d t 2 4 = x + d x d t 2 The order of the differential equation is the order of the highest order derivative present in the equation. Therefore, the order of the given differential equation is 2 . The degree of Differential Equation is the power of the highest order derivative. Therefore, degree of the given differential equation is 4 .

Write down, showing reasons, the order and degree of d 3 x d t 3 2 + y = 1 + d y d x 3 .

Given differential equation d 3 x d t 3 2 + y = 1 + d y d x 3 ⇒ d 3 x d t 3 2 + y 3 = 1 + d y d x 3 3 ⇒ d 3 x d t 3 6 + y 3 + 3 y d 3 x d t 3 d 3 x d t 3 + y = 1 + d y d x The order of the differential equation is the order of the highest order derivative present in the equation. Therefore, the order of the given differential equation is 3 . The degree of Differential Equation is the power of the highest order derivative. Therefore, degree of the given differential equation is 6 .

Write down, showing reasons, the order and degree of y = x d y d x 2 + d x d y 2 .

Given differential equation y = x d y d x 2 + d x d y 2 ⇒ y = x d y d x 2 + 1 d y d x 2 ⇒ y d y d x 2 = x d y d x 4 + 1 The order of the differential equation is the order of the highest order derivative present in the equation. Therefore, the order of the given differential equation is 1 . The degree of Differential Equation is the power of the highest order derivative. Therefore, degree of the given differential equation is 4 .