Solve
`(y+sinxcos^(2)(xy))/(cos^(2)(xy))dx+((x)/(cos^(2)(xy))+siny)dy=0.`

Solve dy/dx+(2xy)/(1+x^(2))=(4x^(2))/(1+x^(2))

Solve (dy)/(dx)+xy=xy^(2)

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

The solution of differential equation xdy(y^(2)e^(xy)+e^(x//y))=ydx(e^(x//y)-y^(2)e^(xy)), is

y=sqrt(1+x^(2)) and y'=(xy)/(1+x^(2))

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

If x^(2)+xy+y^(2)=0, (d^(2)y)/(dx^(2))=

If x^(2) + xy+ y^(2) =0 , (d^(2)y)/(dx^(2))