Internal problem ID [5781]
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 A. Drill exercises. Page
400
Problem number: 3(b).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=x \relax (t )+y \relax (t )\\ y^{\prime }\relax (t )&=-x \relax (t )+y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 34
dsolve([diff(x(t),t)=x(t)+y(t),diff(y(t),t)=-x(t)+y(t)],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = -{\mathrm e}^{t} \left (\cos \relax (t ) c_{1}-c_{2} \sin \relax (t )\right ) \] \[ y \relax (t ) = {\mathrm e}^{t} \left (c_{2} \cos \relax (t )+\sin \relax (t ) c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 39
DSolve[{x'[t]==x[t]+y[t],y'[t]==-x[t]+y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^t (c_1 \cos (t)+c_2 \sin (t)) \\ y(t)\to e^t (c_2 \cos (t)-c_1 \sin (t)) \\ \end{align*}