78.29.4 problem 1 (d)

Internal problem ID [18483]
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 60. Critical Points and Stability for Linear Systems. Problems at page 539
Problem number : 1 (d)
Date solved : Tuesday, January 28, 2025 at 11:50:42 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )&=5 x \left (t \right )+2 y\\ y^{\prime }&=-17 x \left (t \right )-5 y \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 49

dsolve([diff(x(t),t)=5*x(t)+2*y(t),diff(y(t),t)=-17*x(t)-5*y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= \sin \left (3 t \right ) c_{1} +\cos \left (3 t \right ) c_{2} \\ y &= \frac {3 \cos \left (3 t \right ) c_{1}}{2}-\frac {3 \sin \left (3 t \right ) c_{2}}{2}-\frac {5 \sin \left (3 t \right ) c_{1}}{2}-\frac {5 \cos \left (3 t \right ) c_{2}}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 58

DSolve[{D[x[t],t]==5*x[t]+2*y[t],D[y[t],t]==-17*x[t]-5*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to c_1 \cos (3 t)+\frac {1}{3} (5 c_1+2 c_2) \sin (3 t) \\ y(t)\to c_2 \cos (3 t)-\frac {1}{3} (17 c_1+5 c_2) \sin (3 t) \\ \end{align*}