Internal problem ID [6543]
Internal file name [OUTPUT/5791_Sunday_June_05_2022_03_54_40_PM_17429521/index.tex]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven
Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 10. Systems of First-Order Equations. Section B. Challenge Problems. Page
401
Problem number: 2.
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 )&=t y \left (t \right )+1\\ y^{\prime }\left (t \right )&=-x \left (t \right ) t +y \left (t \right ) \end {align*}
With initial conditions \[ [x \left (0\right ) = 0, y \left (0\right ) = -1] \] Does not currently support non autonomous system of first order linear differential equations. The following is the phase plot
✗ Solution by Maple
dsolve([diff(x(t),t) = t*y(t)+1, diff(y(t),t) = -t*x(t)+y(t), x(0) = 0, y(0) = -1], singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{x'[t]==x[t]*y[t]+1,y'[t]==-x[t]+y[t]},{x[0]==2,y[0]==-1},{x[t],y[t]},t,IncludeSingularSolutions -> True]
Not solved