Internal problem ID [5782]
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 }\relax (t )&=3 x \relax (t )-5 y \relax (t )\\ y^{\prime }\relax (t )&=-x \relax (t )+2 y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.093 (sec). Leaf size: 86
dsolve([diff(x(t),t)=3*x(t)-5*y(t),diff(y(t),t)=-x(t)+2*y(t)],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = -\frac {c_{1} {\mathrm e}^{\frac {\left (5+\sqrt {21}\right ) t}{2}} \sqrt {21}}{2}+\frac {c_{2} {\mathrm e}^{-\frac {\left (-5+\sqrt {21}\right ) t}{2}} \sqrt {21}}{2}-\frac {c_{1} {\mathrm e}^{\frac {\left (5+\sqrt {21}\right ) t}{2}}}{2}-\frac {c_{2} {\mathrm e}^{-\frac {\left (-5+\sqrt {21}\right ) t}{2}}}{2} \] \[ y \relax (t ) = c_{1} {\mathrm e}^{\frac {\left (5+\sqrt {21}\right ) t}{2}}+c_{2} {\mathrm e}^{-\frac {\left (-5+\sqrt {21}\right ) t}{2}} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 126
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}{21} e^{5 t/2} \left (21 c_1 \cosh \left (\frac {\sqrt {21} t}{2}\right )+\sqrt {21} (c_1-10 c_2) \sinh \left (\frac {\sqrt {21} t}{2}\right )\right ) \\ y(t)\to \frac {1}{42} e^{-\frac {1}{2} \left (\sqrt {21}-5\right ) t} \left (c_2 \left (-\left (\sqrt {21}-21\right ) e^{\sqrt {21} t}+21+\sqrt {21}\right )-2 \sqrt {21} c_1 \left (e^{\sqrt {21} t}-1\right )\right ) \\ \end{align*}