Calculus

Calculus Level 2

If \(f''(x)=-f(x)\) and \(g(x)=f'(x)\) and \(F(x)= \left(f \left(\dfrac x2\right)\right)^2+\left(g \left(\dfrac x2\right)\right)^2\) and given that \(F(5)=5\), find \(F(10)\).

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