Internal problem ID [5960]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 8 SYSTEMS OF LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS.
EXERCISES 8.1. Page 332
Problem number: 3.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=-3 x \relax (t )+4 y \relax (t )-9 z \relax (t )\\ y^{\prime }\relax (t )&=6 x \relax (t )-y \relax (t )\\ z^{\prime }\relax (t )&=10 x \relax (t )+4 y \relax (t )+3 z \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.787 (sec). Leaf size: 3007
dsolve([diff(x(t),t)=-3*x(t)+4*y(t)-9*z(t),diff(y(t),t)=6*x(t)-y(t),diff(z(t),t)=10*x(t)+4*y(t)+3*z(t)],[x(t), y(t), z(t)], singsol=all)
\[ \text {Expression too large to display} \] \[ \text {Expression too large to display} \] \[ z \relax (t ) = c_{2} {\mathrm e}^{-\frac {\left (170-\left (4726+306 \sqrt {291}\right )^{\frac {2}{3}}+2 \left (4726+306 \sqrt {291}\right )^{\frac {1}{3}}\right ) t}{6 \left (4726+306 \sqrt {291}\right )^{\frac {1}{3}}}} \sin \left (\frac {\left (\left (4726+306 \sqrt {291}\right )^{\frac {2}{3}}+170\right ) t \sqrt {3}\, 1156^{\frac {1}{3}}}{204 \left (139+9 \sqrt {291}\right )^{\frac {1}{3}}}\right )+c_{3} {\mathrm e}^{-\frac {\left (170-\left (4726+306 \sqrt {291}\right )^{\frac {2}{3}}+2 \left (4726+306 \sqrt {291}\right )^{\frac {1}{3}}\right ) t}{6 \left (4726+306 \sqrt {291}\right )^{\frac {1}{3}}}} \cos \left (\frac {\left (\left (4726+306 \sqrt {291}\right )^{\frac {2}{3}}+170\right ) t \sqrt {3}\, 1156^{\frac {1}{3}}}{204 \left (139+9 \sqrt {291}\right )^{\frac {1}{3}}}\right )+c_{1} {\mathrm e}^{-\frac {\left (\left (4726+306 \sqrt {291}\right )^{\frac {2}{3}}+\left (4726+306 \sqrt {291}\right )^{\frac {1}{3}}-170\right ) t}{3 \left (4726+306 \sqrt {291}\right )^{\frac {1}{3}}}} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 510
DSolve[{x'[t]==-3*x[t]+4*y[t]-9*z[t],y'[t]==6*x[t]-y[t],z'[t]==10*x[t]+4*y[t]+3*z[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to 4 c_2 \text {RootSum}\left [\text {$\#$1}^3+\text {$\#$1}^2+57 \text {$\#$1}+369\&,\frac {\text {$\#$1} e^{\text {$\#$1} t}-12 e^{\text {$\#$1} t}}{3 \text {$\#$1}^2+2 \text {$\#$1}+57}\&\right ]-9 c_3 \text {RootSum}\left [\text {$\#$1}^3+\text {$\#$1}^2+57 \text {$\#$1}+369\&,\frac {\text {$\#$1} e^{\text {$\#$1} t}+e^{\text {$\#$1} t}}{3 \text {$\#$1}^2+2 \text {$\#$1}+57}\&\right ]+c_1 \text {RootSum}\left [\text {$\#$1}^3+\text {$\#$1}^2+57 \text {$\#$1}+369\&,\frac {\text {$\#$1}^2 e^{\text {$\#$1} t}-2 \text {$\#$1} e^{\text {$\#$1} t}-3 e^{\text {$\#$1} t}}{3 \text {$\#$1}^2+2 \text {$\#$1}+57}\&\right ] \\ y(t)\to -54 c_3 \text {RootSum}\left [\text {$\#$1}^3+\text {$\#$1}^2+57 \text {$\#$1}+369\&,\frac {e^{\text {$\#$1} t}}{3 \text {$\#$1}^2+2 \text {$\#$1}+57}\&\right ]+6 c_1 \text {RootSum}\left [\text {$\#$1}^3+\text {$\#$1}^2+57 \text {$\#$1}+369\&,\frac {\text {$\#$1} e^{\text {$\#$1} t}-3 e^{\text {$\#$1} t}}{3 \text {$\#$1}^2+2 \text {$\#$1}+57}\&\right ]+c_2 \text {RootSum}\left [\text {$\#$1}^3+\text {$\#$1}^2+57 \text {$\#$1}+369\&,\frac {\text {$\#$1}^2 e^{\text {$\#$1} t}+81 e^{\text {$\#$1} t}}{3 \text {$\#$1}^2+2 \text {$\#$1}+57}\&\right ] \\ z(t)\to 4 c_2 \text {RootSum}\left [\text {$\#$1}^3+\text {$\#$1}^2+57 \text {$\#$1}+369\&,\frac {\text {$\#$1} e^{\text {$\#$1} t}+13 e^{\text {$\#$1} t}}{3 \text {$\#$1}^2+2 \text {$\#$1}+57}\&\right ]+2 c_1 \text {RootSum}\left [\text {$\#$1}^3+\text {$\#$1}^2+57 \text {$\#$1}+369\&,\frac {5 \text {$\#$1} e^{\text {$\#$1} t}+17 e^{\text {$\#$1} t}}{3 \text {$\#$1}^2+2 \text {$\#$1}+57}\&\right ]+c_3 \text {RootSum}\left [\text {$\#$1}^3+\text {$\#$1}^2+57 \text {$\#$1}+369\&,\frac {\text {$\#$1}^2 e^{\text {$\#$1} t}+4 \text {$\#$1} e^{\text {$\#$1} t}-21 e^{\text {$\#$1} t}}{3 \text {$\#$1}^2+2 \text {$\#$1}+57}\&\right ] \\ \end{align*}