ODE No. 1928

\[ \left \{x''(t)=\frac {k x(t)}{\left (x(t)^2+y(t)^2\right )^{3/2}},y''(t)=\frac {k y(t)}{\left (x(t)^2+y(t)^2\right )^{3/2}}\right \} \] Mathematica : cpu = 0.0058821 (sec), leaf count = 0

DSolve[{Derivative[2][x][t] == (k*x[t])/(x[t]^2 + y[t]^2)^(3/2), Derivative[2][y][t] == (k*y[t])/(x[t]^2 + y[t]^2)^(3/2)},{x[t], y[t]},t]
 

, could not solve

DSolve[{Derivative[2][x][t] == (k*x[t])/(x[t]^2 + y[t]^2)^(3/2), Derivative[2][y][t] == (k*y[t])/(x[t]^2 + y[t]^2)^(3/2)}, {x[t], y[t]}, t]

Maple : cpu = 0. (sec), leaf count = 0

dsolve({diff(diff(x(t),t),t) = k*x(t)/(x(t)^2+y(t)^2)^(3/2), diff(diff(y(t),t),t) = k*y(t)/(x(t)^2+y(t)^2)^(3/2)})
 

, exception

time expired