Internal problem ID [5970]
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: 13.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=-x \relax (t )+\frac {y \relax (t )}{4}\\ y^{\prime }\relax (t )&=x \relax (t )-y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 36
dsolve([diff(x(t),t)=-x(t)+1/4*y(t),diff(y(t),t)=x(t)-y(t)],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = \frac {c_{1} {\mathrm e}^{-\frac {t}{2}}}{2}-\frac {c_{2} {\mathrm e}^{-\frac {3 t}{2}}}{2} \] \[ y \relax (t ) = c_{1} {\mathrm e}^{-\frac {t}{2}}+c_{2} {\mathrm e}^{-\frac {3 t}{2}} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 63
DSolve[{x'[t]==-x[t]+1/4*y[t],y'[t]==x[t]-y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{4} e^{-3 t/2} \left (2 c_1 \left (e^t+1\right )+c_2 \left (e^t-1\right )\right ) \\ y(t)\to e^{-t} \left (c_2 \cosh \left (\frac {t}{2}\right )+2 c_1 \sinh \left (\frac {t}{2}\right )\right ) \\ \end{align*}