`(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^(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)

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

(d^(2)y)/(dx^(2))+(dy)/(dx)+y=(1-e^(x))^(2)

If R=([1+((dy)/(dx))^2]^(3//2))/((d^2y)/(dx2)) , thenR^(2//3) can be put in the form of 1/(((d^2y)/(dx^2))^(2//3))+1/(((d^2x)/(dy^2))^(2//3)) b. 1/(((d^2y)/(dx^2))^(2//3))-1/(((d^2x)/(dy^2))^(2//3)) c. 2/(((d^2y)/(dx^2))^(2//3))+2/(((d^2x)/(dy^2))^(2//3)) d. 1/(((d^2y)/(dx^2))^(2//3))dot1/(((d^2x)/(dy^2))^(2//3))

If e^(y)(x+1)=1 ,show that (d^(2)y)/(dx^(2))=((dy)/(dx))^(2)

If e^(y)(x+1)=1, show that (d^(2)y)/(dx^(2))=((dy)/(dx))^(2)

If y=x log((x)/(a+bx)), thenx ^(3)(d^(2)y)/(dx^(2))= (a) x(dy)/(dx)-y (b) (x(dy)/(dx)-y)^(2)y(dy)/(dx)-x(d)(y(dy)/(dx)-x)^(2)

find the order and degree of D.E : (1) ((d^(2)y)/(dx^(2) ))^2 + ((dy)/(dx))^(3) = e^(x) (2) sqrt(1 + 1/((dy)/(dx))^(2))= ((d^(2)y)/(dx^(2)))^(3/2) (3) e^((dy)/(dx))+ (dy)/(dx) =x

Find degree and order x(d^(2)y)/(dx^(2))+((dy)/(dx))^(5)-y(dy)/(dx)=3

[" The differential equation of the family of curves "],[y=c_(1)x^(3)+(c_(2))/(x)" where "c_(1)" and "c_(2)" are arbitrary "],[" constants,is "],[" O "x^(2)(d^(2)y)/(dx^(2))-x(dy)/(dx)-3y=0],[" (x) "(d^(2)y)/(dx^(2))+x(dy)/(dx)+3y=0],[" (x) "(d^(2)y)/(dx^(2))+x(dy)/(dx)-3y=0],[" (x) "(d^(2)y)/(dx^(2))-x(dy)/(dx)+3y=0]