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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