Internal problem ID [5789]
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: 1.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=x \relax (t ) y \relax (t )+1\\ y^{\prime }\relax (t )&=-x \relax (t )+y \relax (t ) \end {align*}
With initial conditions \[ [x \relax (0) = 2, y \relax (0) = -1] \]
✗ Solution by Maple
dsolve([diff(x(t),t) = x(t)*y(t)+1, diff(y(t),t) = -x(t)+y(t), x(0) = 2, y(0) = -1],[x(t), y(t)], 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