Internal problem ID [1602]
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 14.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\left (t \right )&=3 y_{1} \left (t \right )+2 y_{2} \left (t \right )-2 y_{3} \left (t \right )\\ y_{2}^{\prime }\left (t \right )&=-2 y_{1} \left (t \right )+7 y_{2} \left (t \right )-2 y_{3} \left (t \right )\\ y_{3}^{\prime }\left (t \right )&=-10 y_{1} \left (t \right )+10 y_{2} \left (t \right )-5 y_{3} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 57
dsolve([diff(y__1(t),t)=3*y__1(t)+2*y__2(t)-2*y__3(t),diff(y__2(t),t)=-2*y__1(t)+7*y__2(t)-2*y__3(t),diff(y__3(t),t)=-10*y__1(t)+10*y__2(t)-5*y__3(t)],singsol=all)
\begin{align*} y_{1} \left (t \right ) &= c_{2} {\mathrm e}^{5 t}+c_{3} {\mathrm e}^{-5 t} \\ y_{2} \left (t \right ) &= c_{2} {\mathrm e}^{5 t}+c_{3} {\mathrm e}^{-5 t}+{\mathrm e}^{5 t} c_{1} \\ y_{3} \left (t \right ) &= 5 c_{3} {\mathrm e}^{-5 t}+{\mathrm e}^{5 t} c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 126
DSolve[{y1'[t]==3*y1[t]+2*y2[t]-2*y3[t],y2'[t]==-2*y1[t]+7*y2[t]-2*y3[t],y1'[t]==-10*y1[t]+10*y2[t]-5*y3[t]},{y1[t],y2[t],y3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to -\frac {e^{5 t} \left (c_1 \left (432 e^{10 t/3}-1331\right )+c_2 \left (1331-216 e^{10 t/3}\right )\right )}{85184} \\ \text {y2}(t)\to -\frac {e^{5 t} \left (c_1 \left (216 e^{10 t/3}-1331\right )+c_2 \left (1331-108 e^{10 t/3}\right )\right )}{42592} \\ \text {y3}(t)\to \frac {e^{5 t} \left (c_1 \left (720 e^{10 t/3}+1331\right )-c_2 \left (360 e^{10 t/3}+1331\right )\right )}{85184} \\ \end{align*}