If `y=logx` then `(dy)/(dx)=`

If y=x^((logx)^log(logx)) then (dy)/(dx)=

If y=x^(logx)+(logx)^x then find (dy)/(dx)

For each of the following initial value problems verify that the accompanying functions is a solution. (i) x(dy)/(dx)=1,\ y(1)=0 => y=logx (ii) (dy)/(dx)=y ,\ y(0)=1 => y=e^x (iii) (d^2y)/(dx^2)+y=0,\ y(0)=0,\ y^(prime)(0)=1 => y=sinx (iv) (d^2y)/(dx^2)-(dy)/(dx)=0,\ y(0)=2,\ y^(prime)(0)=1 => y=e^x+1

If x^y=e^(x-y) , then (dy)/(dx) is (a) (1+x)/(1+logx) (b) (1-logx)/(1+logx) (c) not defined (d) (logx)/((1+logx)^2)

If y=e^(sin^(-1)x)" and "u=logx," then"(dy)/(du), is

If y=acos(logx) , find (dy)/(dx) .

For each of the differential equations given below, indicate its order and degree (if defined).(i) (d^2y)/(dx^2)+5x((dy)/(dx))^2-6x y=logx (ii) ((dy)/(dx))^3-4((dy)/(dx))^2+7y=sinx (iii) (d^4y)/(dx^4)-sin((d^3y)/(dx^3))=0

The solution of the equation (dy)/(dx)=(x(2logx+1))/(siny+ycosy) is

The solution of the equation (dy)/(dx)=(x(2logx+1))/(siny+ycosy) is

Find one parameter families of solution curves of the following differential equations: (or solve the following differential equations): (a) (dy)/(dx)cos^2x=tanx-y (b) xlogx \ (dy)/(dx)+y=2logx