7.22.7 problem 17

Internal problem ID [582]
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 : 17
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 )&=6 x-y \left (t \right ) \end{align*}

With initial conditions

\begin{align*} x \left (0\right ) = 1\\ y \left (0\right ) = 2 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 17

dsolve([diff(x(t),t) = y(t), diff(y(t),t) = 6*x(t)-y(t), x(0) = 1, y(0) = 2], singsol=all)
 

\begin{align*} x \left (t \right ) &= {\mathrm e}^{2 t} \\ y \left (t \right ) &= 2 \,{\mathrm e}^{2 t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 20

DSolve[{D[x[t],t]==y[t],D[y[t],t]==6*x[t]-y[t]},{x[0]==1,y[0]==2},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to e^{2 t} \\ y(t)\to 2 e^{2 t} \\ \end{align*}