If `y=e^-x cos2x` then which of the following differential equations is satisfied?

Solve the following differential equations. (e^y+1)cos x dx+e^y sin x dy=0

For each of the following differential equation find the particular solution satisfying the given condition. (e^y+1)cos x+e^y sinx dy/dx=0 when x=(pi)/6 , y=0 .

For each of the following differential equation find the particular solution satisfying the given condition. y.(1+log x)dx/dy-x log x=0,y=e^2 ,where x=e.

Find one parameter families of solution curves of the following differential equations: (or solve the following differential equations): (dy)/(dx)-y=cos2x x(dy)/(dx)+y=x^3

Solve the following differential equations: y e^(x//y)dx=(x e^(x/y)+y)dy

Solve the following differential equations.(4) (x dy/dx-y)e^(y/x)=x^2 cos x