Internal problem ID [9451]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1876.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=x \left (t \right ) \cos \left (t \right )\\ y^{\prime }\left (t \right )&=x \left (t \right ) {\mathrm e}^{-\sin \left (t \right )} \end {align*}
✓ Solution by Maple
Time used: 0.296 (sec). Leaf size: 18
dsolve([diff(x(t),t)=x(t)*cos(t),diff(y(t),t)=x(t)*exp(-sin(t))],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = c_{1} {\mathrm e}^{\sin \left (t \right )} \] \[ y \left (t \right ) = c_{1} t +c_{2} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 22
DSolve[{x'[t]==x[t]*Cos[t],y'[t]==x[t]*Exp[-Sin[t]]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 e^{\sin (t)} \\ y(t)\to c_1 t+c_2 \\ \end{align*}