Internal problem ID [1614]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 10 Linear system of Differential equations. Section 10.5, constant coefficient
homogeneous system II. Page 555
Problem number: section 10.5, problem 11.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\relax (t )&=4 y_{1}\relax (t )-2 y_{2}\relax (t )-2 y_{3}\relax (t )\\ y_{2}^{\prime }\relax (t )&=-2 y_{1}\relax (t )+3 y_{2}\relax (t )-y_{3}\relax (t )\\ y_{3}^{\prime }\relax (t )&=2 y_{1}\relax (t )-y_{2}\relax (t )+3 y_{3}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.058 (sec). Leaf size: 69
dsolve([diff(y__1(t),t)=4*y__1(t)-2*y__2(t)-2*y__3(t),diff(y__2(t),t)=-2*y__1(t)+3*y__2(t)-1*y__3(t),diff(y__3(t),t)=2*y__1(t)-1*y__2(t)+3*y__3(t)],[y__1(t), y__2(t), y__3(t)], singsol=all)
\[ y_{1}\relax (t ) = -2 c_{1} {\mathrm e}^{2 t}+\frac {c_{3} {\mathrm e}^{4 t}}{2} \] \[ y_{2}\relax (t ) = -3 c_{1} {\mathrm e}^{2 t}-c_{2} {\mathrm e}^{4 t}-c_{3} {\mathrm e}^{4 t} t \] \[ y_{3}\relax (t ) = c_{1} {\mathrm e}^{2 t}+c_{2} {\mathrm e}^{4 t}+c_{3} {\mathrm e}^{4 t} t \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 125
DSolve[{y1'[t]==4*y1[t]-2*y2[t]-2*y3[t],y2'[t]==-2*y1[t]+3*y2[t]-1*y3[t],y3'[t]==2*y1[t]-1*y2[t]+3*y3[t]},{y1[t],y2[t],y3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to e^{2 t} \left (-(-c_1+c_2+c_3) e^{2 t}+c_2+c_3\right ) \\ \text {y2}(t)\to \frac {1}{2} \left (3 (c_2+c_3) e^{2 t}-e^{4 t} (4 (c_1-c_2-c_3) t+c_2+3 c_3)\right ) \\ \text {y3}(t)\to -\frac {1}{2} e^{2 t} \left (-e^{2 t} (4 (c_1-c_2-c_3) t+c_2+3 c_3)+c_2+c_3\right ) \\ \end{align*}