`y=x^(3)-4x^(2)+5`. Find ` (dy)/(dx) , (d^(2) y)/(dx^(2))` and ` (d^(3)y)/(dx^(3))` .

If y=x^(4) , find (d^(2)y)/(dx^(2))and(d^(3)y)/(dx^(3)) .

If y=x^(4) , find (d^(2)y)/(dx^(2))and(d^(3)y)/(dx^(3)) .

The differential equation representing the family of curves given by y=ae^(-3x)+b , where a and b are arbitrary constants, is a) (d^(2)y)/(dx^(2))+3(dy)/(dx)-2y=0 b) (d^(2)y)/(dx^(2))-3(dy)/(dx)=0 c) (d^(2)y)/(dx^(2))-3(dy)/(dx)-2y=0 d) (d^(2)y)/(dx^(2))+3(dy)/(dx)=0

The order and degree of the differential equation [((dy)/(dx))^(2) + ((d^(2)y)/(dx^(2)))]^(5//4) = k (d^(3) y)/(dx^(3)) is

(x^(2)d^(2)y)/(dx^(2))=(x(dy)/(dx)-y)^(3) Find Degree.

If y= 3e^(2x)+ 2e^(3x) ,then (d^(2)y)/(dx^(2))-5(dy)/(dx) =

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

find order and degree [(d^(3)y)/(dx^(3)) +x]^(5/2) = (d^(2)y)/(dx^(2))

What is the degree of the differential equation ((d^(4)y)/(dx^(4)))^(3/2) -5 "" (d^(3) y)/(dx^(3)) + 6 "" (d^(2) y)/(dx^(2)) -8 "" (dy)/(dx) + 5 = 0 ?

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