Internal problem ID [342]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 7.3, The eigenvalue method for linear systems. Page 395
Problem number: problem 39.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right )+9 x_{4} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )+2 x_{2} \left (t \right )-10 x_{4} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=-x_{3} \left (t \right )+8 x_{4} \left (t \right )\\ x_{4}^{\prime }\left (t \right )&=x_{4} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 61
dsolve([diff(x__1(t),t)=-2*x__1(t)+0*x__2(t)+0*x__3(t)+9*x__4(t),diff(x__2(t),t)=4*x__1(t)+2*x__2(t)+0*x__3(t)-10*x__4(t),diff(x__3(t),t)=0*x__1(t)+0*x__2(t)-1*x__3(t)+8*x__4(t),diff(x__4(t),t)=0*x__1(t)+0*x__2(t)+0*x__3(t)+1*x__4(t)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= 3 c_{4} {\mathrm e}^{t}+c_{2} {\mathrm e}^{-2 t} \\ x_{2} \left (t \right ) &= c_{1} {\mathrm e}^{2 t}-2 c_{4} {\mathrm e}^{t}-c_{2} {\mathrm e}^{-2 t} \\ x_{3} \left (t \right ) &= 4 c_{4} {\mathrm e}^{t}+c_{3} {\mathrm e}^{-t} \\ x_{4} \left (t \right ) &= c_{4} {\mathrm e}^{t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 103
DSolve[{x1'[t]==-2*x1[t]+0*x2[t]+0*x3[t]+9*x4[t],x2'[t]==4*x1[t]+2*x2[t]+0*x3[t]-10*x4[t],x3'[t]==0*x1[t]+0*x2[t]-1*x3[t]+8*x4[t],x4'[t]==0*x1[t]+0*x2[t]+0*x3[t]+1*x4[t]},{x1[t],x2[t],x3[t],x4[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^{-2 t} \left (3 c_4 \left (e^{3 t}-1\right )+c_1\right ) \\ \text {x2}(t)\to e^{-2 t} \left (c_1 \left (e^{4 t}-1\right )+(c_2-c_4) e^{4 t}-2 c_4 e^{3 t}+3 c_4\right ) \\ \text {x3}(t)\to e^{-t} \left (4 c_4 \left (e^{2 t}-1\right )+c_3\right ) \\ \text {x4}(t)\to c_4 e^t \\ \end{align*}