52.10.35 problem 38

Internal problem ID [8429]
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 : 38
Date solved : Monday, January 27, 2025 at 04:00:25 PM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )&=x \left (t \right )-8 y\\ y^{\prime }&=x \left (t \right )-3 y \end{align*}

✓ Solution by Maple

Time used: 0.021 (sec). Leaf size: 59

dsolve([diff(x(t),t)=x(t)-8*y(t),diff(y(t),t)=x(t)-3*y(t)],singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 64

DSolve[{D[x[t],t]==x[t]-8*y[t],D[y[t],t]==x[t]-3*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to e^{-t} (c_1 \cos (2 t)+(c_1-4 c_2) \sin (2 t)) \\ y(t)\to \frac {1}{2} e^{-t} (2 c_2 \cos (2 t)+(c_1-2 c_2) \sin (2 t)) \\ \end{align*}