Internal problem ID [1603]
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 15.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\left (t \right )&=3 y_{1} \left (t \right )+y_{2} \left (t \right )-y_{3} \left (t \right )\\ y_{2}^{\prime }\left (t \right )&=3 y_{1} \left (t \right )+5 y_{2} \left (t \right )+y_{3} \left (t \right )\\ y_{3}^{\prime }\left (t \right )&=-6 y_{1} \left (t \right )+2 y_{2} \left (t \right )+4 y_{3} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 54
dsolve([diff(y__1(t),t)=3*y__1(t)+1*y__2(t)-1*y__3(t),diff(y__2(t),t)=3*y__1(t)+5*y__2(t)+1*y__3(t),diff(y__3(t),t)=-6*y__1(t)+2*y__2(t)+4*y__3(t)],[y__1(t), y__2(t), y__3(t)], singsol=all)
\[ y_{1} \left (t \right ) = -\frac {c_{3} {\mathrm e}^{6 t}}{2}+\frac {c_{2}}{2}+\frac {{\mathrm e}^{6 t} c_{1}}{3} \] \[ y_{2} \left (t \right ) = -\frac {c_{2}}{2}-\frac {c_{3} {\mathrm e}^{6 t}}{2}+{\mathrm e}^{6 t} c_{1} \] \[ y_{3} \left (t \right ) = c_{2} +c_{3} {\mathrm e}^{6 t} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 93
DSolve[{y1'[t]==3*y1[t]+1*y2[t]-1*y3[t],y2'[t]==3*y1[t]+5*y2[t]+1*y3[t],y1'[t]==-6*y1[t]+2*y2[t]+4*y3[t]},{y1[t],y2[t],y3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to \frac {1}{625} \left (-\left (c_1 \left (e^{6 t}-500\right )\right )-c_2 \left (e^{6 t}+125\right )\right ) \text {y2}(t)\to \frac {1}{625} \left (c_2 \left (125-4 e^{6 t}\right )-4 c_1 \left (e^{6 t}+125\right )\right ) \text {y3}(t)\to \frac {1}{625} \left (-\left (c_1 \left (e^{6 t}-1000\right )\right )-c_2 \left (e^{6 t}+250\right )\right ) \end{align*}