Another differential equation problem

Calculus Level 5

We have a continous,differentiable curve passing through $$(0,1)$$ defined as $$f(x,y)=0$$ satisfying the property that the area made by tangent and normal to the curve at any point on the curve $$(x,y)$$ and the x-axis is equal to the magnitude of the ordinate(i.e. $$=\left| y\right|$$ ).

There are exactly two possible curves satisfying the condition. One is bounded and the other one is unbounded curves.

Let the area bounded by the bounded curve and the y-axis be = $$a-\frac{b\pi}{c}$$,where $$a,b,c$$ are positive integers and $$b,c$$ are co-prime.

Find $$a+b+c$$

Details and assumptions

1) I am saying unbounded curve in the sense that for some x either y is tending to infinity or for some y,x is tending to infinity.

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