Internal problem ID [1640]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 10 Linear system of Differential equations. Section 10.6, constant coefficient
homogeneous system III. Page 566
Problem number: section 10.6, problem 5.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\relax (t )&=-3 y_{1}\relax (t )-3 y_{2}\relax (t )+y_{3}\relax (t )\\ y_{2}^{\prime }\relax (t )&=2 y_{2}\relax (t )+2 y_{3}\relax (t )\\ y_{3}^{\prime }\relax (t )&=5 y_{1}\relax (t )+y_{2}\relax (t )+y_{3}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 1.212 (sec). Leaf size: 2728
dsolve([diff(y__1(t),t)=-3*y__1(t)-3*y__2(t)+1*y__3(t),diff(y__2(t),t)=0*y__1(t)+2*y__2(t)+2*y__3(t),diff(y__3(t),t)=5*y__1(t)+1*y__2(t)+1*y__3(t)],[y__1(t), y__2(t), y__3(t)], singsol=all)
\[ \text {Expression too large to display} \] \[ \text {Expression too large to display} \] \[ y_{3}\relax (t ) = c_{2} \sin \left (\frac {\left (\left (540+6 \sqrt {6042}\right )^{\frac {2}{3}}-42\right ) t \sqrt {3}\, 36^{\frac {1}{3}}}{36 \left (90+\sqrt {6042}\right )^{\frac {1}{3}}}\right ) {\mathrm e}^{\frac {\left (\left (540+6 \sqrt {6042}\right )^{\frac {2}{3}}+42\right ) t}{6 \left (540+6 \sqrt {6042}\right )^{\frac {1}{3}}}}+c_{3} \cos \left (\frac {\left (\left (540+6 \sqrt {6042}\right )^{\frac {2}{3}}-42\right ) t \sqrt {3}\, 36^{\frac {1}{3}}}{36 \left (90+\sqrt {6042}\right )^{\frac {1}{3}}}\right ) {\mathrm e}^{\frac {\left (\left (540+6 \sqrt {6042}\right )^{\frac {2}{3}}+42\right ) t}{6 \left (540+6 \sqrt {6042}\right )^{\frac {1}{3}}}}+c_{1} {\mathrm e}^{-\frac {\left (\left (540+6 \sqrt {6042}\right )^{\frac {2}{3}}+42\right ) t}{3 \left (540+6 \sqrt {6042}\right )^{\frac {1}{3}}}} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 177
DSolve[{y1'[t]==3*y1[t]-3*y2[t]+1*y3[t],y2'[t]==0*y1[t]+2*y2[t]+2*y3[t],y3'[t]==5*y1[t]+1*y2[t]+1*y3[t]},{y1[t],y2[t],y3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to \frac {1}{4} e^{-2 t} \left (e^{6 t} ((3 c_1-c_2+c_3) \cos (2 t)+(c_1-3 c_2-c_3) \sin (2 t))+c_1+c_2-c_3\right ) \\ \text {y2}(t)\to \frac {1}{4} e^{-2 t} \left (e^{6 t} ((-c_1+3 c_2+c_3) \cos (2 t)+(3 c_1-c_2+c_3) \sin (2 t))+c_1+c_2-c_3\right ) \\ \text {y3}(t)\to \frac {1}{2} e^{-2 t} \left (e^{6 t} ((c_1+c_2+c_3) \cos (2 t)+2 (c_1-c_2) \sin (2 t))-c_1-c_2+c_3\right ) \\ \end{align*}