7.18.11 problem 11

Internal problem ID [540]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 4. Laplace transform methods. Section 4.2 (Transformation of initial value problems). Problems at page 287
Problem number : 11
Date solved : Monday, January 27, 2025 at 02:54:41 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }&=2 x+y \left (t \right )\\ y^{\prime }\left (t \right )&=6 x+3 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: 0.020 (sec). Leaf size: 9

dsolve([diff(x(t),t) = 2*x(t)+y(t), diff(y(t),t) = 6*x(t)+3*y(t), x(0) = 1, y(0) = -2], singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 10

DSolve[{D[x[t],t]==2*x[t]+y[t],D[y[t],t]==6*x[t]+3*y[t]},{x[0]==1,y[0]==-2},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to 1 \\ y(t)\to -2 \\ \end{align*}