Internal problem ID [776]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 7.8, Repeated Eigenvalues. page 436
Problem number: 11.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=x_{1}\relax (t )\\ x_{2}^{\prime }\relax (t )&=-4 x_{1}\relax (t )+x_{2}\relax (t )\\ x_{3}^{\prime }\relax (t )&=3 x_{1}\relax (t )+6 x_{2}\relax (t )+2 x_{3}\relax (t ) \end {align*}
With initial conditions \[ [x_{1}\relax (0) = -1, x_{2}\relax (0) = 2, x_{3}\relax (0) = -30] \]
✓ Solution by Maple
Time used: 0.042 (sec). Leaf size: 40
dsolve([diff(x__1(t),t) = x__1(t), diff(x__2(t),t) = -4*x__1(t)+x__2(t), diff(x__3(t),t) = 3*x__1(t)+6*x__2(t)+2*x__3(t), x__1(0) = -1, x__2(0) = 2, x__3(0) = -30],[x__1(t), x__2(t), x__3(t)], singsol=all)
\[ x_{1}\relax (t ) = -{\mathrm e}^{t} \] \[ x_{2}\relax (t ) = -\frac {{\mathrm e}^{t} \left (-192 t -96\right )}{48} \] \[ x_{3}\relax (t ) = 3 \,{\mathrm e}^{2 t}-33 \,{\mathrm e}^{t}-24 t \,{\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 39
DSolve[{x1'[t]==1*x1[t]+0*x2[t]+0*x3[t],x2'[t]==-4*x1[t]+1*x2[t]+0*x3[t],x3'[t]==3*x1[t]+6*x2[t]+2*x3[t]},{x1[0]==-1,x2[0]==2,x3[0]==-30},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to -e^t \\ \text {x2}(t)\to 2 e^t (2 t+1) \\ \text {x3}(t)\to 3 e^t \left (-8 t+e^t-11\right ) \\ \end{align*}