Internal problem ID [14026]
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.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=4 x \left (t \right )+2 y \left (t \right )\\ y^{\prime }\left (t \right )&=3 x \left (t \right )-y \left (t \right ) \end {align*}
With initial conditions \[ [x \left (0\right ) = 0, y \left (0\right ) = -21] \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 34
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}^{-2 t}-6 \,{\mathrm e}^{5 t} \\ y \left (t \right ) &= -18 \,{\mathrm e}^{-2 t}-3 \,{\mathrm e}^{5 t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 36
DSolve[{x'[t]==4*x[t]+2*y[t],y'[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*}