Verify the differential equation `y = x sin x : xy' = y + x sqrt(x^(2) - y^(2))(x ne 0 and x gt y or x lt -y)`

Verify the differential equation y = Ax : xy' = y (x ne 0)

Verify that the given functions ( explicit or implicit ) is a solution of the corresponding differential equation : y=xsinx : xy'=y+xsqrt(x^(2)-y^(2)) (xne0"and"x lt y"or"x gt -y)

The differential of y if y=sin 2x is

Solve the differential equation y e^(x)/(y) dx = (x e^(x)/(y) + y^(2))dy ( y ne 0) .

The differential of y if y=sin 2x is ………… .

An equation of the curve satisfying x dy - y dx = sqrt(x^(2)-y^(2))dx and y(1) = 0 is

Find the particular solution of the differential equation (dy)/(dx) + y cot x = 2x + x^(2) cot x( x ne 0) given that y = 0 when x = (pi)/(2) .

Find the general solution of the differential equation x (dy)/(dx) + 2y = x^(2)(x ne 0) .

Differentiate : (i) y = sin (x^2) (ii) y = sin^2 x

y = sqrt(a^(2) - x^(2)) x ne (-a, a) : x + y (dy)/(dx) = 0(y ne 0)