Solve `(x+y(dy)/(dx))/(y-x(dy)/(dx))=x^2+2y^2+(y^4)/(x^2)`

Solve y-x(dy)/(dx)=a(y^(2)+(dy)/(dx))

Solve (dy)/(dx)=(y)/(2y log y+y-x).

Solve (x+y)^(2)(dy)/(dx)=a^(2)

Solve (dy)/(dx)+(y)/(x)=log x.

Solve (dy)/(dx)=sin^(2) (x+3y)+5

Solve (dy)/(dx)+3y =e^(-2x) .

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

Solve (dy)/(dx)+2y=cos x.