Internal problem ID [10198]
Internal file name [OUTPUT/9145_Monday_June_06_2022_06_45_02_AM_97098396/index.tex]
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.
The type(s) of ODE detected by this program : "system of linear ODEs" Unable to solve or complete the solution.
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*}
Does not currently support non autonomous system of first order linear differential equations. The following is the phase plot
✓ Solution by Maple
Time used: 0.141 (sec). Leaf size: 18
dsolve([diff(x(t),t)=x(t)*cos(t),diff(y(t),t)=x(t)*exp(-sin(t))],singsol=all)
\begin{align*} x \left (t \right ) &= c_{2} {\mathrm e}^{\sin \left (t \right )} \\ y \left (t \right ) &= c_{2} t +c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.005 (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*}