Let \(2{ \left( f\left( x \right) \right) }^{ 2 }-\frac { { d }^{ 2 }f\left( x \right) }{ d{ x }^{ 2 } } f\left( x \right) +{ \left( \frac { df\left( x \right) }{ dx } \right) }^{ 2 }=0\)
and \(f\left( 0 \right) =f\left( 1 \right) =-1\)

Then the area of the region bounded by y=0, x=0, x=1 and \(y=\left( 2x-1 \right) f\left( x \right)\) is \(2\left( 1-\frac { 1 }{ { e }^{ { 1 }/{ a } } } \right)\)

Then the value of a is???

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