Sketch the curve for y=x

We know that, general solution of ==n+(-1)n, n=0,1,2,...

Here,

y=x

y=n+(-1)nx

When n=0,even, then (-1)n=1, so y=n+x, n=0,2,.....

When n=odd, then (-1)n=-1, so y=n-x,n=1,3,....

y=n+x and y=n-x are perpendicular to each other clearly. 

So the solution is an infinite number of straight lines. 

Hence the sketch of the curve for y=x is