Internal problem ID [5790]
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.
Solve \begin {align*} x^{\prime }\relax (t )&=y \relax (t ) t +1\\ y^{\prime }\relax (t )&=-x \relax (t ) t +y \relax (t ) \end {align*}
With initial conditions \[ [x \relax (0) = 0, y \relax (0) = -1] \]
✗ 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],[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