64.18.1 problem 1

Internal problem ID [13624]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 7, Systems of linear differential equations. Section 7.4. Exercises page 309
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 05:54:03 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=5 x \left (t \right )-2 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=4 x \left (t \right )-y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.038 (sec). Leaf size: 30

dsolve([diff(x(t),t)=5*x(t)-2*y(t),diff(y(t),t)=4*x(t)-y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{3 t}+c_{2} {\mathrm e}^{t} \\ y \left (t \right ) &= c_{1} {\mathrm e}^{3 t}+2 c_{2} {\mathrm e}^{t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 63

DSolve[{D[x[t],t]==5*x[t]-2*y[t],D[y[t],t]==4*x[t]-y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to e^t \left (c_1 \left (2 e^{2 t}-1\right )-c_2 \left (e^{2 t}-1\right )\right ) \\ y(t)\to e^t \left (2 c_1 \left (e^{2 t}-1\right )-c_2 \left (e^{2 t}-2\right )\right ) \\ \end{align*}