78.28.6 problem 1 (f)

Internal problem ID [18476]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 10. Systems of First Order Equations. Section 56. Homogeneous Linear Systems with Constant Coefficients. Problems at page 505
Problem number : 1 (f)
Date solved : Tuesday, January 28, 2025 at 11:50:36 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )&=-4 x \left (t \right )-y\\ y^{\prime }&=x \left (t \right )-2 y \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 29

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

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

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 43

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

\begin{align*} x(t)\to e^{-3 t} (c_1 (-t)-c_2 t+c_1) \\ y(t)\to e^{-3 t} ((c_1+c_2) t+c_2) \\ \end{align*}