78.28.7 problem 1 (g)

Internal problem ID [18477]
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 (g)
Date solved : Tuesday, January 28, 2025 at 11:50:37 AM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.016 (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: 0.003 (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*}