60.10.10 problem 1922

Internal problem ID [11921]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 9, system of higher order odes
Problem number : 1922
Date solved : Monday, January 27, 2025 at 11:47:21 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=-y \left (t \right )+\left (\left \{\begin {array}{cc} x \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}-1\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 )\\ \frac {d}{d t}y \left (t \right )&=x \left (t \right )+\left (\left \{\begin {array}{cc} y \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}-1\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: 0.000 (sec). Leaf size: 0

DSolve[{D[x[t],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}}],D[y[t],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