Internal problem ID [9455]
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 }\relax (t )&=x \relax (t ) \cos \relax (t )\\ y^{\prime }\relax (t )&=x \relax (t ) {\mathrm e}^{-\sin \relax (t )} \end {align*}
✓ Solution by Maple
Time used: 0.148 (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)
\[ x \relax (t ) = c_{2} {\mathrm e}^{\sin \relax (t )} \] \[ y \relax (t ) = c_{2} t +c_{1} \]
✓ Solution by Mathematica
Time used: 0.004 (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*}