What is the differential equation of the family of parabolas having a vertex at origin and axis along positive y-axis?

What is the solution of the differential equation (dy − dx) + cos x(dy + dx) = 0 ?

What is the degree of the differential equation? $1+\left(\frac{dy}{dx}\right)^2 =\left(\frac{d^2y}{dx^2}\right)^{\frac{4}{3}}?$

If $\frac{dy}{dx} = (\ln 5)y $  with y(0) = ln 5, then what is y(1) equal to?