simple doubts...

1) The graph of f(x)=√1-x² is a semi circle above the x axis.

2)y=C_{1}e^{x+C_{2}}+C_{3}e^{x+C_{4}}+C_{5}\sin (x+C_{6})+C_{7}\cos (x+C_{8})

\Rightarrowy=C_{1}e^{C_{2}}e^{x}+C_{3}e^{C_{4}}e^{x}+C_{5}\sin (x+C_{6})+C_{7}\cos (x+C_{8})

\Rightarrow y=K_{1}e^{x}+C_{5}\sin (x+C_{6})+C_{7}\cos (x+C_{8})

here K_{1}=(C_{1}e^{C_{2}}+C_{3}e^{C_{4}})

\Rightarrow y=K_{1}e^{x}+C_{5}\left\{\sin x\cos C_{6}+\cos x\sin C_{6} \right\}+ C_{7}\left\{\cos x\cos C_{8} -\sin x\sin C_{8}\right\}

\Rightarrow y=K_{1}e^{x}+K_{2}\sin x+K_{3}\cos x

Hence, there are only three independent constants, so order = 3.

Graph of f ( x ) = √ 1 - x ² is not a circle . It is the graph of a semicircle above the x - axis .