Internal problem ID [10245]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 9, system of higher order odes
Problem number: 1922.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-y \left (t \right )+\left (\left \{\begin {array}{cc} x \left (t \right )^{3} \sin \left (\frac {1}{x \left (t \right )^{2}+y \left (t \right )^{2}}\right )+x \left (t \right ) \sin \left (\frac {1}{x \left (t \right )^{2}+y \left (t \right )^{2}}\right ) y \left (t \right )^{2}-x \left (t \right ) \sin \left (\frac {1}{x \left (t \right )^{2}+y \left (t \right )^{2}}\right ) & x \left (t \right )^{2}+y \left (t \right )^{2}\neq 1 \\ 0 & \operatorname {otherwise} \end {array}\right .\right )\\ y^{\prime }\left (t \right )&=x \left (t \right )+\left (\left \{\begin {array}{cc} y \left (t \right ) \sin \left (\frac {1}{x \left (t \right )^{2}+y \left (t \right )^{2}}\right ) x \left (t \right )^{2}+y \left (t \right )^{3} \sin \left (\frac {1}{x \left (t \right )^{2}+y \left (t \right )^{2}}\right )-y \left (t \right ) \sin \left (\frac {1}{x \left (t \right )^{2}+y \left (t \right )^{2}}\right ) & x \left (t \right )^{2}+y \left (t \right )^{2}\neq 1 \\ 0 & \operatorname {otherwise} \end {array}\right .\right ) \end {align*}
✗ Solution by Maple
dsolve([diff(x(t),t)=-y(t)+piecewise((x(t)^2+y(t)^2)<>1,x(t)*(x(t)^2+y(t)^2-1)*sin(1/(x(t)^2+y(t)^2))),diff(y(t),t)=x(t)+piecewise((x(t)^2+y(t)^2)<>1,y(t)*(x(t)^2+y(t)^2-1)*sin(1/(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] + Piecewise[{{x[t]*(x[t]^2 + y[t]^2 - 1)*Sin[1/(x[t]^2 + y[t]^2)], (x[t]^2 + y[t]^2) != 1}, {0, True}}],y'[t] == x[t] + Piecewise[{{y[t]*(x[t]^2 + y[t]^2 - 1)*Sin[1/(x[t]^2 + y[t]^2)], (x[t]^2 + y[t]^2) != 1}, {0, True}}]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
Not solved