Internal problem ID [804]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 9.1, The Phase Plane: Linear Systems. page 505
Problem number: 13.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=x_{1}\relax (t )+x_{2}\relax (t )-2\\ x_{2}^{\prime }\relax (t )&=x_{1}\relax (t )-x_{2}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.141 (sec). Leaf size: 70
dsolve([diff(x__1(t),t)=1*x__1(t)+1*x__2(t)-2,diff(x__2(t),t)=1*x__1(t)-1*x__2(t)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1}\relax (t ) = \sqrt {2}\, {\mathrm e}^{t \sqrt {2}} c_{2}-\sqrt {2}\, {\mathrm e}^{-t \sqrt {2}} c_{1}+{\mathrm e}^{t \sqrt {2}} c_{2}+{\mathrm e}^{-t \sqrt {2}} c_{1}+1 \] \[ x_{2}\relax (t ) = {\mathrm e}^{t \sqrt {2}} c_{2}+{\mathrm e}^{-t \sqrt {2}} c_{1}+1 \]
✓ Solution by Mathematica
Time used: 0.088 (sec). Leaf size: 74
DSolve[{x1'[t]==1*x1[t]+1*x2[t]-2,x2'[t]==1*x1[t]-1*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to c_1 \cosh \left (\sqrt {2} t\right )+\frac {(c_1+c_2) \sinh \left (\sqrt {2} t\right )}{\sqrt {2}}+1 \\ \text {x2}(t)\to c_2 \cosh \left (\sqrt {2} t\right )+\frac {(c_1-c_2) \sinh \left (\sqrt {2} t\right )}{\sqrt {2}}+1 \\ \end{align*}