60.10.16 problem 1928

Internal problem ID [11927]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 9, system of higher order odes
Problem number : 1928
Date solved : Monday, January 27, 2025 at 11:47:23 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d^{2}}{d t^{2}}x \left (t \right )&=\frac {k x \left (t \right )}{\left (x \left (t \right )^{2}+y \left (t \right )^{2}\right )^{{3}/{2}}}\\ \frac {d^{2}}{d t^{2}}y \left (t \right )&=\frac {k y \left (t \right )}{\left (x \left (t \right )^{2}+y \left (t \right )^{2}\right )^{{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: 0.000 (sec). Leaf size: 0

DSolve[{D[x[t],{t,2}]==k*x[t]/(x[t]^2+y[t]^2)^(3/2),D[y[t],{t,2}]==k*y[t]/(x[t]^2+y[t]^2)^(3/2)},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

Not solved