7.23.10 problem 10

Internal problem ID [596]
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 5.2 (Applications). Problems at page 345
Problem number : 10
Date solved : Monday, January 27, 2025 at 02:55:08 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }+2 y^{\prime }\left (t \right )&=4 x+5 y \left (t \right )\\ 2 x^{\prime }-y^{\prime }\left (t \right )&=3 x \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 13

dsolve([diff(x(t),t)+2*diff(y(t),t) = 4*x(t)+5*y(t), 2*diff(x(t),t)-diff(y(t),t) = 3*x(t), x(0) = 1, y(0) = -1], singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 16

DSolve[{D[x[t],t]+2*D[y[t],t]==4*x[t]+5*y[t],2*D[x[t],t]-D[y[t],t]==3*x[t]},{x[0]==1,y[0]==-1},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

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