50.28.6 problem 1(f)

Internal problem ID [8193]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 10. Systems of First-Order Equations. Section 10.3 Homogeneous Linear Systems with Constant Coefficients. Page 387
Problem number : 1(f)
Date solved : Monday, January 27, 2025 at 03:45:38 PM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.017 (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: 0.003 (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*}