52.10.5 problem 5

Internal problem ID [8399]
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 : 5
Date solved : Monday, January 27, 2025 at 03:57:32 PM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )&=10 x \left (t \right )-5 y\\ y^{\prime }&=8 x \left (t \right )-12 y \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 35

dsolve([diff(x(t),t)=10*x(t)-5*y(t),diff(y(t),t)=8*x(t)-12*y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{8 t}+c_{2} {\mathrm e}^{-10 t} \\ y &= \frac {2 c_{1} {\mathrm e}^{8 t}}{5}+4 c_{2} {\mathrm e}^{-10 t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 73

DSolve[{D[x[t],t]==10*x[t]-5*y[t],D[y[t],t]==8*x[t]-12*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to \frac {1}{18} e^{-10 t} \left (c_1 \left (20 e^{18 t}-2\right )-5 c_2 \left (e^{18 t}-1\right )\right ) \\ y(t)\to \frac {1}{9} e^{-10 t} \left (4 c_1 \left (e^{18 t}-1\right )-c_2 \left (e^{18 t}-10\right )\right ) \\ \end{align*}