# Play with Curves!

Calculus Level 4

$\frac{dy}{dx} = \frac{ y - x^3 - x^2 - \ln y }{\sin y - x + \frac{x}{y}}$

Given that the slope of a curve passing through $$( 0 , \frac{\pi}{2} )$$ is as shown above.

The equation of curve can be represented as

$\frac{x^a}{b} + \frac{x^c}{d} - exy - f \cos (gy) + hx \ln (iy) = 0,$

where $$a$$, $$b$$, $$c$$, $$d$$, $$e$$, $$f$$, $$g$$, $$h$$, and $$i$$ are positive integers.

Find $$a + b + c + d + e + f + g + h + i$$.

Original.

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