The general solution of the differential equation $$\frac{d y}{d x}=\cos ^2(3 x+y)$$ is $$\tan ^{-1}\left(\frac{\sqrt{3}}{2} \tan (3 x+y)\right)=f(x)$$. Then, $$f(x)=$$

If the general solution of the differential equation $$\cos ^2 x \frac{d y}{d x}+y=\tan x$$ is $$y=\tan x-1+C e^{-\tan x}$$ satisfies $$y\left(\frac{\pi}{4}\right)=1$$, then $$C=$$

Assertion (A) Order of the differential equations of a family of circles with constant radius is two.

Reason (R) An algebraic equation having two arbitrary constants is general solution of a second order differential equation.

If $$l$$ and $$m$$ are order and degree of a differential equation of all the straight lines at constant distance of $$P$$ units from the origin, then $$l m^2+l^2 m=$$