The particular solution of the differential equation \[{{\sin }^{-1}}\left( \frac{{{d}^{2}}y}{d{{x}^{2}}}-1 \right)=x\], where\[y=\frac{dy}{dx}=0\] when\[x=0\], is

\[y=\frac{{{x}^{2}}}{2}+\frac{x}{2}-\sin x\]

\[y=\frac{{{x}^{2}}}{2}+x-\sin x\]

The particular solution of the differential equation \[{{\sin }^{-1}}\

1.	The particular solution of the differential equation \[{{\sin }^{-1}}\left( \frac{{{d}^{2}}y}{d{{x}^{2}}}-1 \right)=x\], where\[y=\frac{dy}{dx}=0\] when\[x=0\], is
A.	\[y={{x}^{2}}+x-\sin x\]
B.	\[y=\frac{{{x}^{2}}}{2}+x-\sin x\]
C.	\[y=\frac{{{x}^{2}}}{2}+\frac{x}{2}-\sin x\]
D.	\[2y={{x}^{2}}+x-\sin x\]
Answer» C. \[y=\frac{{{x}^{2}}}{2}+\frac{x}{2}-\sin x\]

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The particular solution of the differential equation \[{{\sin }^{-1}}\left( \frac{{{d}^{2}}y}{d{{x}^{2}}}-1 \right)=x\], where\[y=\frac{dy}{dx}=0\] when\[x=0\], is

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