question_answer

Let \[f\left( x \right),g\left( x \right)\] be two continuously differentiable function satisfying the relationships \[f'\left( x \right)=g\left( x \right)\] and  \[f''\left( x \right)=-f\left( x \right).\] Let \[h\left( x \right)={{\left[ f\left( x \right) \right]}^{2}}+{{\left[ g\left( x \right) \right]}^{2}}.\] If \[h\left( 0 \right)=5,\] then find value of \[h\left( 10 \right)\].

Answer:

5.00