Internal problem ID [5977]
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 8.2. Page 346
Problem number: 4.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=-\frac {5 x \relax (t )}{2}+2 y \relax (t )\\ y^{\prime }\relax (t )&=\frac {3 x \relax (t )}{4}-2 y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 36
dsolve([diff(x(t),t)=-5/2*x(t)+2*y(t),diff(y(t),t)=3/4*x(t)-2*y(t)],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = \frac {4 c_{1} {\mathrm e}^{-t}}{3}-2 c_{2} {\mathrm e}^{-\frac {7 t}{2}} \] \[ y \relax (t ) = c_{1} {\mathrm e}^{-t}+c_{2} {\mathrm e}^{-\frac {7 t}{2}} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 114
DSolve[{x'[t]==5/2*x[t]+2*y[t],y'[t]==3/4*x[t]-2*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 e^{t/4} \cosh \left (\frac {\sqrt {105} t}{4}\right )+\frac {(9 c_1+8 c_2) e^{t/4} \sinh \left (\frac {\sqrt {105} t}{4}\right )}{\sqrt {105}} \\ y(t)\to \frac {1}{35} e^{t/4} \left (35 c_2 \cosh \left (\frac {\sqrt {105} t}{4}\right )+\sqrt {105} (c_1-3 c_2) \sinh \left (\frac {\sqrt {105} t}{4}\right )\right ) \\ \end{align*}