7.22.10 problem 20

Internal problem ID [585]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 5. Linear systems of differential equations. Section 5.1 (First order systems and applications). Problems at page 335
Problem number : 20
Date solved : Monday, January 27, 2025 at 02:55:04 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }&=y \left (t \right )\\ y^{\prime }\left (t \right )&=-9 x+6 y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 31

dsolve([diff(x(t),t)=y(t),diff(y(t),t)=-9*x(t)+6*y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= {\mathrm e}^{3 t} \left (c_2 t +c_1 \right ) \\ y \left (t \right ) &= {\mathrm e}^{3 t} \left (3 c_2 t +3 c_1 +c_2 \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 45

DSolve[{D[x[t],t]==y[t],D[y[t],t]==-9*x[t]+6*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to e^{3 t} (-3 c_1 t+c_2 t+c_1) \\ y(t)\to e^{3 t} (-9 c_1 t+3 c_2 t+c_2) \\ \end{align*}