Internal problem ID [5958]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 8 SYSTEMS OF LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS.
EXERCISES 8.1. Page 332
Problem number: 1.
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 )&=4 x \relax (t )+8 y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 84
dsolve([diff(x(t),t)=3*x(t)-5*y(t),diff(y(t),t)=4*x(t)+8*y(t)],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = -\frac {{\mathrm e}^{\frac {11 t}{2}} \left (\sqrt {55}\, \sin \left (\frac {\sqrt {55}\, t}{2}\right ) c_{2}-\sqrt {55}\, \cos \left (\frac {\sqrt {55}\, t}{2}\right ) c_{1}+5 \sin \left (\frac {\sqrt {55}\, t}{2}\right ) c_{1}+5 \cos \left (\frac {\sqrt {55}\, t}{2}\right ) c_{2}\right )}{8} \] \[ y \relax (t ) = {\mathrm e}^{\frac {11 t}{2}} \left (\sin \left (\frac {\sqrt {55}\, t}{2}\right ) c_{1}+\cos \left (\frac {\sqrt {55}\, t}{2}\right ) c_{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 113
DSolve[{x'[t]==3*x[t]-5*y[t],y'[t]==4*x[t]+8*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{11} e^{11 t/2} \left (11 c_1 \cos \left (\frac {\sqrt {55} t}{2}\right )-\sqrt {55} (c_1+2 c_2) \sin \left (\frac {\sqrt {55} t}{2}\right )\right ) \\ y(t)\to \frac {1}{55} e^{11 t/2} \left (55 c_2 \cos \left (\frac {\sqrt {55} t}{2}\right )+\sqrt {55} (8 c_1+5 c_2) \sin \left (\frac {\sqrt {55} t}{2}\right )\right ) \\ \end{align*}