50.28.7 problem 1(g)

Internal problem ID [8194]
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(g)
Date solved : Monday, January 27, 2025 at 03:45:39 PM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )&=7 x \left (t \right )+6 y \left (t \right )\\ y^{\prime }\left (t \right )&=2 x \left (t \right )+6 y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 35

dsolve([diff(x(t),t)=7*x(t)+6*y(t),diff(y(t),t)=2*x(t)+6*y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{3 t}+c_{2} {\mathrm e}^{10 t} \\ y &= -\frac {2 c_{1} {\mathrm e}^{3 t}}{3}+\frac {c_{2} {\mathrm e}^{10 t}}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 74

DSolve[{D[x[t],t]==7*x[t]+6*y[t],D[y[t],t]==2*x[t]+6*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to \frac {1}{7} e^{3 t} \left (c_1 \left (4 e^{7 t}+3\right )+6 c_2 \left (e^{7 t}-1\right )\right ) \\ y(t)\to \frac {1}{7} e^{3 t} \left (2 c_1 \left (e^{7 t}-1\right )+c_2 \left (3 e^{7 t}+4\right )\right ) \\ \end{align*}