Internal problem ID [9459]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1880.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=\frac {2 x \relax (t ) \sin \relax (t )-y \relax (t ) t -x \relax (t )}{t \left (\sin \relax (t )-1\right )}\\ y^{\prime }\relax (t )&=-\frac {-\cos \relax (t ) y \relax (t ) t^{2}+\cos \relax (t ) x \relax (t ) t -x \relax (t ) \sin \relax (t )+y \relax (t ) t}{t^{2} \left (\sin \relax (t )-1\right )} \end {align*}
✓ Solution by Maple
Time used: 0.188 (sec). Leaf size: 23
dsolve({t^2*(1-sin(t))*diff(x(t),t)=t*(1-2*sin(t))*x(t)+t^2*y(t),t^2*(1-sin(t))*diff(y(t),t)=(t*cos(t)-sin(t))*x(t)+t*(1-t*cos(t))*y(t)},{x(t), y(t)}, singsol=all)
\[ x \relax (t ) = t \left (t c_{2}+c_{1}\right ) \] \[ y \relax (t ) = c_{1} \sin \relax (t )+t c_{2} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 27
DSolve[{t^2*(1-Sin[t])*x'[t]==t*(1-2*Sin[t])*x[t]+t^2*y[t],t^2*(1-Sin[t])*y'[t]==(t*Cos[t]-Sin[t])*x[t]+t*(1-t*Cos[t])*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to t (c_1 t+c_2) \\ y(t)\to c_1 t+c_2 \sin (t) \\ \end{align*}