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

(dy)/(dx) + y = 1( y ne 1)

(x^(2) - y^(2)) dx + 2xy dy = 0

(x + 3y^(2))(dy)/(dx) = y ( y rt 0) .

x dy - y dx = sqrt(x^(2) + y^(2)) dx

(x - y)dy - (x + y) dx = 0

x(dy)/(dx) - y + x sin ((y)/(x)) = 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)

y dx + (x - y^(2))dy = 0

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