7.22.8 problem 18

Internal problem ID [583]
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 : 18
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 )&=10 x-7 y \left (t \right ) \end{align*}

With initial conditions

\begin{align*} x \left (0\right ) = 2\\ y \left (0\right ) = -7 \end{align*}

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 33

dsolve([diff(x(t),t) = -y(t), diff(y(t),t) = 10*x(t)-7*y(t), x(0) = 2, y(0) = -7], singsol=all)
 

\begin{align*} x \left (t \right ) &= -\frac {11 \,{\mathrm e}^{-5 t}}{3}+\frac {17 \,{\mathrm e}^{-2 t}}{3} \\ y \left (t \right ) &= -\frac {55 \,{\mathrm e}^{-5 t}}{3}+\frac {34 \,{\mathrm e}^{-2 t}}{3} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 44

DSolve[{D[x[t],t]==-y[t],D[y[t],t]==10*x[t]-7*y[t]},{x[0]==2,y[0]==-7},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to \frac {1}{3} e^{-5 t} \left (17 e^{3 t}-11\right ) \\ y(t)\to \frac {1}{3} e^{-5 t} \left (34 e^{3 t}-55\right ) \\ \end{align*}