Let `y=f(x) and x=(1)/(z)." If "(d^(2)y)/(dx^(2))=lamda_(z^(3))(dy)/(dz)+z^(4)(d^(2)y)/(dz^(2))`, then the value of `lamda` is

If x=(1)/(z), y=f(x) and (d^(2)y)/(dx^(2))=kz^(3)(dy)/(dz)+z^(4)(d^(2)y)/(dz^(2)) , then the value of k is -

If x=1/z and y=f(x), then prove that, (d^2f)/(dx^2)=2z^3dy/dz+z^4(d^2y)/(dz^2)

If the dependent variable y is changed to z by the substitution y=tan z and the differential equation (d^(2)y)/(dx^(2))=1+(2(1+y))/(1+y^(2))((dy)/(dx))^(2) is changed to (d^(2)z)/(dx^(2))=cos^(2)z+k((dz)/(dx))^(2), then the value of k equal to

If y=(1)/(a-z) , then (dz)/(dy)=

If the dependent variable y is changed to 'z' by the substitution y=tan z then the differential equation (d^(2)y)/(dx^(2))+1+(2(1+y))/(1+y^(2))((dy)/(dx))^(2) is changed to (d^(2)z)/(dx^(2))=cos^(2)z+k((dz)/(dx))^(2) then find the value of k

If y=sin x^(@) and z=log_(10)x , then the value of ( dy)/(dz) is -

The lines (x-3)/(2) = (y-2)/(3) = (z-1)/(lamda ) and (x-2)/(3) = (y-3)/(2) = (z-2)/(3) lie in a same plane then The value of lamda is

Let y=f(x). phi(x) and z=f'(x). phi'(x) prove that (1)/(y)*(d^(2)y)/(dx^(2))=(1)/(f)*(d^(2)f)/(dx^(2))+(1)/(phi)*(d^(2)phi)/(dx^(2))+(2z)/(f phi)

If y = (lot _(e) x)/(x) and z = log _(e) x, then (d ^(2) y)/(dz^(2)) + (dy)/(dz) =

If y=1/(a-z), " then " (dz)/(dy) is