4. `dy/dx=sinx`

If y=sqrt(cos x+sqrt(cos x +sqrt(cos x+....oo))) " then prove that " dy/dx = sinx /(1-2y).

ysinx dy/dx=(sinx-y^2)cosx

Solve the following differential equations (dy)/(dx)=sinx*siny

Degree and order xy(d^(2)y)/(dx^(2))+((dy)/(dx))^(3)-y(dy)/(dx)=sinx

Solve: (secx)(dy)/(dx)=y+sinx

(dy)/(dx)=2(sinx-cosx)^(-2)

"If "y=sqrt(cosx+sqrt(cosx+sqrt(cosx+...oo)))", prove that "(dy)/(dx)=(sinx)/((2y-1)).

"If "y=(sinx)^(cosx)+(cosx)^(sinx)", prove that "(dy)/(dx)=(sinx)^(cosx).[cot x cos x-sin x(log sinx)]+(cosx)^(sinx).[cosx(log cos x)-sinx tanx].

Order and degree of the differential equation (dy)/(dx)=(2sinx+3)/((dy)/(dx)) respectively are