# Finding "curve"

Calculus Level 4

Let the equation of the curve $$y=f(x)$$ is such that $$\dfrac { { d }^{ 2 }y }{ d{ x }^{ 2 } } =\sqrt { 1-{ \left( \dfrac { dy }{ dx } \right) }^{ 2 } }$$ and the tangent to the curve at the origin is inclined at $$\dfrac{ \pi } { 4}$$ with the postive direction of the $$x$$-axis. Find the value of $$y$$ at $$x= \dfrac { \pi }{2}$$

NOTE:-$$f^{ ' }\left( x \right) \neq constant$$

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