Internal problem ID [6730]
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 }\left (t \right )&=-\frac {5 x \left (t \right )}{2}+2 y\\ y^{\prime }&=\frac {3 x \left (t \right )}{4}-2 y \end {align*}
✓ Solution by Maple
Time used: 0.016 (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)],singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{-\frac {7 t}{2}} c_{1} +c_{2} {\mathrm e}^{-t} \\ y \left (t \right ) &= -\frac {{\mathrm e}^{-\frac {7 t}{2}} c_{1}}{2}+\frac {3 c_{2} {\mathrm e}^{-t}}{4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 165
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 \frac {1}{210} e^{\frac {1}{4} \left (t-\sqrt {105} t\right )} \left (3 c_1 \left (\left (35+3 \sqrt {105}\right ) e^{\frac {\sqrt {105} t}{2}}+35-3 \sqrt {105}\right )+8 \sqrt {105} c_2 \left (e^{\frac {\sqrt {105} t}{2}}-1\right )\right ) \\ y(t)\to \frac {1}{70} e^{\frac {1}{4} \left (t-\sqrt {105} t\right )} \left (\sqrt {105} c_1 \left (e^{\frac {\sqrt {105} t}{2}}-1\right )-c_2 \left (\left (3 \sqrt {105}-35\right ) e^{\frac {\sqrt {105} t}{2}}-35-3 \sqrt {105}\right )\right ) \\ \end{align*}