Internal problem ID [10244]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 9, system of higher order odes
Problem number: 1921.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-x \left (t \right )^{2} y \left (t \right )-y \left (t \right )^{3}\\ y^{\prime }\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} \\ \frac {x \left (t \right )^{3}}{2}-\frac {y \left (t \right )^{4}}{2 x \left (t \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: 0.0 (sec). Leaf size: 0
DSolve[{x'[t]==-y[t]*(x[t]^2+y[t]^2),y'[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