`(d^2x)/(dy^2)` equals: (1) `((d^2y)/(dx^2))^-1` (2) `-((d^2y)/(dx^2))^-1 ((dy)/(dx))^-3` (3) `-((d^2y)/(dx^2))^-1 ((dy)/(dx))^-2` (4) `-((d^2y)/(dx^2))^-1 ((dy)/(dx))^3`

(d^2x)/(dy^2) equals: (1.) ((d^2y)/(dx^2))^-1 (2) -((d^2y)/(dx^2)) ((dy)/(dx))^-3 (3) -((d^2y)/(dx^2))^-1 ((dy)/(dx))^-2 (4) -((d^2y)/(dx^2))^-1 ((dy)/(dx))^3

(d^2x)/(dy^2) equals: (1) ((d^2y)/(dx^2))^(-1) (2) -((d^2y)/(dx^2))^(-1)((dy)/(dx))^(-3) (3) ((d^2y)/(dx^2))^(-1)((dy)/(dx))^(-2) (4) -((d^2y)/(dx^2))((dy)/(dx))^(-3)

(d^(2)x)/(dy^(2)) equals: (1)((d^(2)y)/(dx^(2)))^(-1) (2) -((d^(2)y)/(dx^(2)))^(-1)((dy)/(dx))^(-3)(3)-((d^(2)y)/(dx^(2)))^(-1)((dy)/(dx))^(-2)(4)-((d^(2)y)/(dx^(2)))^(-1)((dy)/(dx))^(3)

(d^(2)x)/(dy^(2)) equals a. ((d^(2)y)/(dx^(2)))^(-1) b. -((d^(2)y)/(dx^(2)))^(-1)((dy)/(dx))^(-3) c. ((d^(2)y)/(dx^(2)))((dy)/(dx))^(-2) d. -((d^(2)y)/(dx^(2)))((dy)/(dx))^(-3)

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

If x=logp and y=1/p ,then (a) (d^2y)/(dx^2)-2p=0 (b) (d^2y)/(dx^2)+y=0 (c) (d^2y)/(dx^2)+(dy)/(dx)=0 (d) (d^2y)/(dx^2)-(dy)/(dx)=0

If x=logp and y=1/p ,then (a) (d^2y)/(dx^2)-2p=0 (b) (d^2y)/(dx^2)+y=0 (c) (d^2y)/(dx^2)+(dy)/(dx)=0 (d) (d^2y)/(dx^2)-(dy)/(dx)=0

If x=logp and y=1/p ,then (a) (d^2y)/(dx^2)-2p=0 (b) (d^2y)/(dx^2)+y=0 (c) (d^2y)/(dx^2)+(dy)/(dx)=0 (d) (d^2y)/(dx^2)-(dy)/(dx)=0

If x=log pandy=(1)/(p), then (a) (d^(2)y)/(dx^(2))-2p=0 (b) (d^(2)y)/(dx^(2))+y=0 (c) (d^(2)y)/(dx^(2))+(dy)/(dx)=0( d) (d^(2)y)/(dx^(2))-(dy)/(dx)=0

Show that (d ^(2)x)/( dy^2) =- ((d ^(2) y )/( dx ^(2))) ((dy)/(dx)) ^(-3)