Solve the following differential equation:

Using properties of determinants, prove the following:

Differentiate the following function w.r.t. x:

(x)^{cos x} + (sin x)^{tan x}

Find the value of so that the following lines are perpendicular to each other.

Find the area of the region enclosed between the two circles

x²+ y² = 9 and (x - 3)² + y² = 9.