If `R=([1+((dy)/(dx))^2]^(3//2))/((d^2y)/(dx2))` , then`R^(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 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

The second derivative of a single valued function parametrically represented by x=varphi(t)a n dy=psi(t) (where varphi(t)a n dpsi(t) are different function and varphi^(prime)(t)!=0 ) is given by (d^2y)/(dx^2)=(((dx)/(dt))((d^2y)/(dt^2))-((d^2x)/(dt^2))((dy)/(dt))/(((dx)/(dt))^2) (d^2y)/(dx^2)=(((dx)/(dt))((d^2y)/(dt^2))-((d^2x)/(dt^2))((dy)/(dt))/(((dx)/(dt))^3) (d^2y)/(dx^2)=(((d^2x)/(dt))((d^y)/(dt^2))-((d^x)/(dt^))((d^2y)/(dt^2))/(((dx)/(dt))^3) (d^2y)/(dx^2)=(((d^2x)/(dt^2))((d^y)/(dt^))-((d^2x)/(dt^2))((d^y)/(dt^))/(((dx)/(dt))^3)

(dy)/(dx)=(sin^(2)x)/(1+x^(3))-(3x^(2))/(1+x^(3))y

The order of the differential equation ((d^(2)y)/(dx^(2)))^(3)=(1+(dy)/(dx))^(1/2) is

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

The degree of the differential equation ((d^(2)y)/(dx^(2)))^(3)+((dy)/(dx))^(2)+1=0 is

If y^2=P(x) , then 2d/dx(y^3(d^2y/dx^2))

Solve (d^2y)/(dx^2)=((dy)/(dx))^2

Determine its order, degree (if exists) ((d^(3)y)/(dx^(3)))^((2)/(3))-3(d^(2)y)/(dx^(2))+5(dy)/(dx)+4=0

The order and degree of the differential equation [((d^(2)y)/(dx^(2)))+((dy)/(dx))^(2)]^((1)/(2))=(d^(3)y)/(dx^(3)) are