find a differential equation with trig function and constant in angle

Question

I am trying to find the equation for this solution. $y = x *\tan(x + c)$
When I take the derivative I get
$y' = \tan(x+c)+x*\sec(x+c)^2$
I do not see how I can get c out from the trig functions and determine its value,
to substitute in the solution.

Answer 1

$$y = x *\tan(x + c)$$ For $x \ne 0$ $$\arctan (\frac yx)=x+c$$ Implicit differentiation gives $$\frac 1 {1+\frac {y^2}{x^2}}(\frac yx)' =1$$ $$y'x-y=x^2+y^2$$

Answer 2

Hint: $$\tan^2(x)+1=\sec^2(x)$$