Internal problem ID [1601]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 10 Linear system of Differential equations. Section 10.4, constant coefficient
homogeneous system. Page 540
Problem number: section 10.4, problem 13.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\relax (t )&=-2 y_{1}\relax (t )+2 y_{2}\relax (t )-6 y_{3}\relax (t )\\ y_{2}^{\prime }\relax (t )&=2 y_{1}\relax (t )+6 y_{2}\relax (t )+2 y_{3}\relax (t )\\ y_{3}^{\prime }\relax (t )&=-2 y_{1}\relax (t )-2 y_{2}\relax (t )+2 y_{3}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 67
dsolve([diff(y__1(t),t)=-2*y__1(t)+2*y__2(t)-6*y__3(t),diff(y__2(t),t)=2*y__1(t)+6*y__2(t)+2*y__3(t),diff(y__3(t),t)=-2*y__1(t)-2*y__2(t)+2*y__3(t)],[y__1(t), y__2(t), y__3(t)], singsol=all)
\[ y_{1}\relax (t ) = -c_{1} {\mathrm e}^{4 t}-c_{2} {\mathrm e}^{6 t}+4 c_{3} {\mathrm e}^{-4 t} \] \[ y_{2}\relax (t ) = -c_{2} {\mathrm e}^{6 t}-c_{3} {\mathrm e}^{-4 t} \] \[ y_{3}\relax (t ) = c_{1} {\mathrm e}^{4 t}+c_{2} {\mathrm e}^{6 t}+c_{3} {\mathrm e}^{-4 t} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 192
DSolve[{y1'[t]==-2*y1[t]+2*y2[t]-6*y3[t],y2'[t]==2*y1[t]+6*y2[t]+2*y3[t],y1'[t]==-2*y1[t]-2*y2[t]+2*y3[t]},{y1[t],y2[t],y3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to \frac {e^{5 t/2} \left (73 (198 c_1+25 c_2) \cosh \left (\frac {\sqrt {73} t}{2}\right )-\sqrt {73} (1682 c_1+171 c_2) \sinh \left (\frac {\sqrt {73} t}{2}\right )\right )}{299008} \\ \text {y2}(t)\to -\frac {e^{5 t/2} \left (73 (50 c_1+27 c_2) \cosh \left (\frac {\sqrt {73} t}{2}\right )+\sqrt {73} (143 c_2-342 c_1) \sinh \left (\frac {\sqrt {73} t}{2}\right )\right )}{299008} \\ \text {y3}(t)\to -\frac {e^{5 t/2} \left (73 (50 c_1+27 c_2) \cosh \left (\frac {\sqrt {73} t}{2}\right )+\sqrt {73} (143 c_2-342 c_1) \sinh \left (\frac {\sqrt {73} t}{2}\right )\right )}{598016} \\ \end{align*}