\[
\boxed{
 \left\{ {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}x \left( t \right) ={\frac {kx \left( t \right) }{ \left(  \left( x \left( t \right)  \right) ^{2}+ \left( y \left( t \right)  \right) ^{2} \right) ^{3/2}}},{\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}y \left( t \right) ={\frac {ky \left( t \right) }{ \left(  \left( x \left( t \right)  \right) ^{2}+ \left( y \left( t \right)  \right) ^{2} \right) ^{3/2}}} \right\} }
\]