If `y=y(x)` and it follows the relation `e^(xy)+y cos x=2,` then

If y=y(x) and it follows the relation 4x e^(x y)=y+5sin^2x , then y^(prime)(0) is equal to______

Differentiate : y=e^x cos x

Find the order and degree, if defined, of each of the following differential equations: (i) (dy)/(dx) - cos x = 0 (ii) xy (d^(2)y)/(dx^(2)) + x((dy)/(dx))^(2) - y (dy)/(dx) = 0 (iii) y''' + y^(2) + e^(y)' = 0

If (x,y) lies on the ellipse x^(2)+2y^(3) = 2 , then maximum value of x^(2)+y^(2)+ sqrt(2)xy - 1 is

For each of the functions find the f _(x), f _(y), and show that f _(xy) = f _(yx). f (x,y) = cos (x ^(2) - 3xy )

Differentiate the following with respect to x : y =e^(x cos x)

Find the differential equation for the following y = e^(3x) (A cos 2x+B sin 2x)