Find the order and degree of the following D.E's
(i) `(d^(2)y)/(dx^(2)) + 2((dy)/(dx))^(2) + 5y = 0`
(ii) `2(d^(2)y)/(dx^(2)) = (5+(dy)/(dx))^((5)/(3))`
(iii) `1+((d^(2)y)/(dx^(2)))^(2) = [2+((dy)/(dx))^(2)]^((3//2))`
(iv) `[(d^(2)y)/(dx^(2))+((dy)/(dx))^(3)]^((6/(5))` = `6y`
(v) `[((dy)/(dx))^(2) + (d^(2)y)/(dx^(2))]^((7)/(3)) = (d^(3y))/(dx^(3))`
(vi) `[((dy)/(dx))^((1)/(2)) + ((d^(2)y)/(dx^(2)))^((1)/(2))]^((1)/(4)) = 0`
(vii) `(d^(2)y)/(dx^(2)) + p^(2)y = 0`
(viii) `((d^(3)y)/(dx^(3)))^(2) -3((dy)/(dx))^(2) - e^(x) = 4`

Answer

(i) ordered 2 degree 1 (ii) order 2 , degree 3
(iii) order 2, degree 4 (iv) order 2, degree 6
(v) order 3, degree 3 (vi) order 2, degree 1/2
(vii) order 2, degree 1 (viii) order 3, degree 2