60.10.9 problem 1921

Internal problem ID [11920]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 9, system of higher order odes
Problem number : 1921
Date solved : Monday, January 27, 2025 at 11:47:20 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=-y \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right )\\ \frac {d}{d t}y \left (t \right )&=\left \{\begin {array}{cc} x \left (t \right )^{2}+y \left (t \right )^{2} & 2 x \left (t \right )\le x \left (t \right )^{2}+y \left (t \right )^{2} \\ \left (\frac {x \left (t \right )}{2}-\frac {y \left (t \right )^{2}}{2 x \left (t \right )}\right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right ) & \operatorname {otherwise} \end {array}\right . \end{align*}

✗ Solution by Maple

dsolve([diff(x(t),t)=-y(t)*(x(t)^2+y(t)^2),diff(y(t),t)=piecewise((x(t)^2+y(t)^2)>=2*x(t),(x(t)^2+y(t)^2),(x(t)/2-y(t)^2/(2*x(t)))*(x(t)^2+y(t)^2))],singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

Not solved