Internal problem ID [786]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 7.9, Nonhomogeneous Linear Systems. page 447
Problem number: 9.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=-\frac {5 x_{1}\relax (t )}{4}+\frac {3 x_{2}\relax (t )}{4}+2 t\\ x_{2}^{\prime }\relax (t )&=\frac {3 x_{1}\relax (t )}{4}-\frac {5 x_{2}\relax (t )}{4}+{\mathrm e}^{t} \end {align*}
✓ Solution by Maple
Time used: 0.043 (sec). Leaf size: 51
dsolve([diff(x__1(t),t)=-5/4*x__1(t)+3/4*x__2(t)+2*t,diff(x__2(t),t)=3/4*x__1(t)-5/4*x__2(t)+exp(t)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1}\relax (t ) = c_{2} {\mathrm e}^{-\frac {t}{2}}-c_{1} {\mathrm e}^{-2 t}-\frac {17}{4}+\frac {{\mathrm e}^{t}}{6}+\frac {5 t}{2} \] \[ x_{2}\relax (t ) = c_{2} {\mathrm e}^{-\frac {t}{2}}+c_{1} {\mathrm e}^{-2 t}+\frac {3 t}{2}-\frac {15}{4}+\frac {{\mathrm e}^{t}}{2} \]
✓ Solution by Mathematica
Time used: 0.357 (sec). Leaf size: 101
DSolve[{x1'[t]==-5/4*x1[t]+3/4*x2[t]+2*t,x2'[t]==3/4*x1[t]-5/4*x2[t]+Exp[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{12} \left (30 t+2 e^t+6 (c_1-c_2) e^{-2 t}+6 (c_1+c_2) e^{-t/2}-51\right ) \\ \text {x2}(t)\to \frac {1}{4} e^{-2 t} \left (3 e^{2 t} (2 t-5)+2 e^{3 t}+2 (c_1+c_2) e^{3 t/2}-2 c_1+2 c_2\right ) \\ \end{align*}