50.29.1 problem 2(a)

Internal problem ID [8197]
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 A. Drill exercises. Page 400
Problem number : 2(a)
Date solved : Monday, January 27, 2025 at 03:45:41 PM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )&=3 x \left (t \right )-4 y \left (t \right )\\ y^{\prime }\left (t \right )&=4 x \left (t \right )-7 y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.021 (sec). Leaf size: 31

dsolve([diff(x(t),t)=3*x(t)-4*y(t),diff(y(t),t)=4*x(t)-7*y(t)],singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 73

DSolve[{D[x[t],t]==3*x[t]-4*y[t],D[y[t],t]==4*x[t]-7*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to \frac {1}{3} e^{-5 t} \left (c_1 \left (4 e^{6 t}-1\right )-2 c_2 \left (e^{6 t}-1\right )\right ) \\ y(t)\to \frac {1}{3} e^{-5 t} \left (2 c_1 \left (e^{6 t}-1\right )-c_2 \left (e^{6 t}-4\right )\right ) \\ \end{align*}