Internal problem ID [12821]
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: 18.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-10 x \left (t \right )+10 y\\ y^{\prime }&=28 x \left (t \right )-y\\ z^{\prime }\left (t \right )&=-\frac {8 z \left (t \right )}{3} \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 95
dsolve([diff(x(t),t)=-10*x(t)+10*y(t)+0*z(t),diff(y(t),t)=28*x(t)-1*y(t)+0*z(t),diff(z(t),t)=0*x(t)+0*y(t)-8/3*z(t)],[x(t), y(t), z(t)], singsol=all)
\begin{align*} x \left (t \right ) = \frac {c_{1} {\mathrm e}^{\frac {\left (-11+\sqrt {1201}\right ) t}{2}} \sqrt {1201}}{56}-\frac {c_{2} {\mathrm e}^{-\frac {\left (11+\sqrt {1201}\right ) t}{2}} \sqrt {1201}}{56}-\frac {9 c_{1} {\mathrm e}^{\frac {\left (-11+\sqrt {1201}\right ) t}{2}}}{56}-\frac {9 c_{2} {\mathrm e}^{-\frac {\left (11+\sqrt {1201}\right ) t}{2}}}{56} y \left (t \right ) = c_{1} {\mathrm e}^{\frac {\left (-11+\sqrt {1201}\right ) t}{2}}+c_{2} {\mathrm e}^{-\frac {\left (11+\sqrt {1201}\right ) t}{2}} z \left (t \right ) = c_{3} {\mathrm e}^{-\frac {8 t}{3}} \end{align*}
✓ Solution by Mathematica
Time used: 0.047 (sec). Leaf size: 312
DSolve[{x'[t]==-10*x[t]+10*y[t]+0*z[t],y'[t]==28*x[t]-1*y[t]+0*z[t],z'[t]==0*x[t]+0*y[t]-8/3*z[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {e^{-\frac {1}{2} \left (11+\sqrt {1201}\right ) t} \left (c_1 \left (\left (1201-9 \sqrt {1201}\right ) e^{\sqrt {1201} t}+1201+9 \sqrt {1201}\right )+20 \sqrt {1201} c_2 \left (e^{\sqrt {1201} t}-1\right )\right )}{2402} y(t)\to \frac {e^{-\frac {1}{2} \left (11+\sqrt {1201}\right ) t} \left (56 \sqrt {1201} c_1 \left (e^{\sqrt {1201} t}-1\right )+c_2 \left (\left (1201+9 \sqrt {1201}\right ) e^{\sqrt {1201} t}+1201-9 \sqrt {1201}\right )\right )}{2402} z(t)\to c_3 e^{-8 t/3} x(t)\to \frac {e^{-\frac {1}{2} \left (11+\sqrt {1201}\right ) t} \left (c_1 \left (\left (1201-9 \sqrt {1201}\right ) e^{\sqrt {1201} t}+1201+9 \sqrt {1201}\right )+20 \sqrt {1201} c_2 \left (e^{\sqrt {1201} t}-1\right )\right )}{2402} y(t)\to \frac {e^{-\frac {1}{2} \left (11+\sqrt {1201}\right ) t} \left (56 \sqrt {1201} c_1 \left (e^{\sqrt {1201} t}-1\right )+c_2 \left (\left (1201+9 \sqrt {1201}\right ) e^{\sqrt {1201} t}+1201-9 \sqrt {1201}\right )\right )}{2402} z(t)\to 0 \end{align*}