Internal problem ID [6535]
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(c).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=3 x \left (t \right )-5 y \left (t \right )\\ y^{\prime }\left (t \right )&=-x \left (t \right )+2 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 86
dsolve([diff(x(t),t)=3*x(t)-5*y(t),diff(y(t),t)=-x(t)+2*y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{\frac {\left (5+\sqrt {21}\right ) t}{2}}+c_{2} {\mathrm e}^{-\frac {\left (-5+\sqrt {21}\right ) t}{2}} \\ y \left (t \right ) &= -\frac {c_{1} {\mathrm e}^{\frac {\left (5+\sqrt {21}\right ) t}{2}} \sqrt {21}}{10}+\frac {c_{2} {\mathrm e}^{-\frac {\left (-5+\sqrt {21}\right ) t}{2}} \sqrt {21}}{10}+\frac {c_{1} {\mathrm e}^{\frac {\left (5+\sqrt {21}\right ) t}{2}}}{10}+\frac {c_{2} {\mathrm e}^{-\frac {\left (-5+\sqrt {21}\right ) t}{2}}}{10} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 144
DSolve[{x'[t]==3*x[t]-5*y[t],y'[t]==-x[t]+2*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{42} e^{-\frac {1}{2} \left (\sqrt {21}-5\right ) t} \left (c_1 \left (\left (21+\sqrt {21}\right ) e^{\sqrt {21} t}+21-\sqrt {21}\right )-10 \sqrt {21} c_2 \left (e^{\sqrt {21} t}-1\right )\right ) \\ y(t)\to -\frac {1}{42} e^{-\frac {1}{2} \left (\sqrt {21}-5\right ) t} \left (2 \sqrt {21} c_1 \left (e^{\sqrt {21} t}-1\right )+c_2 \left (\left (\sqrt {21}-21\right ) e^{\sqrt {21} t}-21-\sqrt {21}\right )\right ) \\ \end{align*}