Internal problem ID [13130]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 3. Linear Systems. Exercises section 3.8 page 371
Problem number: 5.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-2 x \left (t \right )+3 y\\ y^{\prime }&=3 x \left (t \right )-2 y\\ z^{\prime }\left (t \right )&=-z \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 40
dsolve([diff(x(t),t)=-2*x(t)+3*y(t)+0*z(t),diff(y(t),t)=3*x(t)-2*y(t)+0*z(t),diff(z(t),t)=0*x(t)+0*y(t)-1*z(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{-5 t}+c_{2} {\mathrm e}^{t} \\ y \left (t \right ) &= -c_{1} {\mathrm e}^{-5 t}+c_{2} {\mathrm e}^{t} \\ z \left (t \right ) &= c_{3} {\mathrm e}^{-t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 150
DSolve[{x'[t]==-2*x[t]+3*y[t]+0*z[t],y'[t]==3*x[t]-2*y[t]+0*z[t],z'[t]==0*x[t]+0*y[t]-1*z[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{2} e^{-5 t} \left (c_1 \left (e^{6 t}+1\right )+c_2 \left (e^{6 t}-1\right )\right ) \\ y(t)\to \frac {1}{2} e^{-5 t} \left (c_1 \left (e^{6 t}-1\right )+c_2 \left (e^{6 t}+1\right )\right ) \\ z(t)\to c_3 e^{-t} \\ x(t)\to \frac {1}{2} e^{-5 t} \left (c_1 \left (e^{6 t}+1\right )+c_2 \left (e^{6 t}-1\right )\right ) \\ y(t)\to \frac {1}{2} e^{-5 t} \left (c_1 \left (e^{6 t}-1\right )+c_2 \left (e^{6 t}+1\right )\right ) \\ z(t)\to 0 \\ \end{align*}