Internal problem ID [6711]
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 }\left (t \right )&=3 x \left (t \right )-5 y\\ y^{\prime }&=4 x \left (t \right )+8 y \end {align*}
✓ Solution by Maple
Time used: 0.031 (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)],singsol=all)
\begin{align*} x \left (t \right ) &= {\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 ) \\ y \left (t \right ) &= \frac {{\mathrm e}^{\frac {11 t}{2}} \left (\sin \left (\frac {\sqrt {55}\, t}{2}\right ) \sqrt {55}\, c_{2} -\cos \left (\frac {\sqrt {55}\, t}{2}\right ) \sqrt {55}\, 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 )}{10} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.025 (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*}