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

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)

Differential equation y log y dx - x dy = 0

Verify that the given functions ( explicit or implicit ) is a solution of the corresponding differential equation : y=Ax:xy'=y(xne0)

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

Show that y = sin ( m sin^(-1)x) is a solution of the differential equation (1 - x^(2)) y '' + xy' + m^(2) y = 0

Solve the differential equation dx/dy​=xy+3x+y+3

Show that y = (cos^(-1) x)^(2) is a solution of the differential equation . (1-x^(2))y '' - xy' - 2 = 0

Find the general solution of the differential equation (dy)/(dx) = (x+1)/(2 - y), (y ne 2) .

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) .

The general solution of the differential equation (y dx - x dy)/(y ) = 0 is