73.27.6 problem 38.6

Internal problem ID [15762]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 38. Systems of differential equations. A starting point. Additional Exercises. page 786
Problem number : 38.6
Date solved : Tuesday, January 28, 2025 at 08:06:47 AM
CAS classification : system_of_ODEs

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

With initial conditions

\begin{align*} x \left (0\right ) = 0\\ y \left (0\right ) = -21 \end{align*}

✓ Solution by Maple

Time used: 0.042 (sec). Leaf size: 33

dsolve([diff(x(t),t) = 4*x(t)+2*y(t), diff(y(t),t) = 3*x(t)-y(t), x(0) = 0, y(0) = -21], singsol=all)
 

\begin{align*} x \left (t \right ) &= -6 \,{\mathrm e}^{5 t}+6 \,{\mathrm e}^{-2 t} \\ y \left (t \right ) &= -3 \,{\mathrm e}^{5 t}-18 \,{\mathrm e}^{-2 t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 36

DSolve[{D[x[t],t]==4*x[t]+2*y[t],D[y[t],t]==3*x[t]-y[t]},{x[0]==0,y[0]==-21},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to -6 e^{-2 t} \left (e^{7 t}-1\right ) \\ y(t)\to -3 e^{-2 t} \left (e^{7 t}+6\right ) \\ \end{align*}