Internal problem ID [330]
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 16.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=-50 x_{1} \relax (t )+20 x_{2} \relax (t )\\ x_{2}^{\prime }\relax (t )&=100 x_{1} \relax (t )-60 x_{2} \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 36
dsolve([diff(x__1(t),t)=-50*x__1(t)+20*x__2(t),diff(x__2(t),t)=100*x__1(t)-60*x__2(t)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1} \relax (t ) = \frac {c_{1} {\mathrm e}^{-10 t}}{2}-\frac {2 c_{2} {\mathrm e}^{-100 t}}{5} \] \[ x_{2} \relax (t ) = c_{1} {\mathrm e}^{-10 t}+c_{2} {\mathrm e}^{-100 t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 74
DSolve[{x1'[t]==-50*x1[t]+20*x2[t],x2'[t]==100*x1[t]-60*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{9} e^{-100 t} \left ((5 c_1+2 c_2) e^{90 t}+4 c_1-2 c_2\right ) \\ \text {x2}(t)\to \frac {1}{9} e^{-100 t} \left (10 c_1 \left (e^{90 t}-1\right )+c_2 \left (4 e^{90 t}+5\right )\right ) \\ \end{align*}