Internal problem ID [10251]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 9, system of higher order odes
Problem number: 1928.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime \prime }\left (t \right )&=\frac {k x \left (t \right )}{\left (x \left (t \right )^{2}+y \left (t \right )^{2}\right )^{\frac {3}{2}}}\\ y^{\prime \prime }\left (t \right )&=\frac {k y \left (t \right )}{\left (x \left (t \right )^{2}+y \left (t \right )^{2}\right )^{\frac {3}{2}}} \end {align*}
✗ Solution by Maple
dsolve([diff(x(t),t,t)=k*x(t)/(x(t)^2+y(t)^2)^(3/2),diff(y(t),t,t)=k*y(t)/(x(t)^2+y(t)^2)^(3/2)],singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{x''[t]==k*x[t]/(x[t]^2+y[t]^2)^(3/2),y''[t]==k*y[t]/(x[t]^2+y[t]^2)^(3/2)},{x[t],y[t]},t,IncludeSingularSolutions -> True]
Not solved