Internal problem ID [6534]
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 }\left (t \right )&=x \left (t \right )+y \left (t \right )\\ y^{\prime }\left (t \right )&=-x \left (t \right )+y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.047 (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)
\[ x \left (t \right ) = -{\mathrm e}^{t} \left (\cos \left (t \right ) c_{1} -\sin \left (t \right ) c_{2} \right ) \] \[ y \left (t \right ) = {\mathrm e}^{t} \left (c_{2} \cos \left (t \right )+c_{1} \sin \left (t \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (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*}