Internal problem ID [12393]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A.
Dobrushkin. CRC Press 2015
Section: Chapter 8.4 Systems of Linear Differential Equations (Method of Undetermined
Coefficients). Problems page 520
Problem number: Problem 1(b).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=9 x \left (t \right )-3 y-6 t\\ y^{\prime }&=-x \left (t \right )+11 y+10 t \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 44
dsolve([diff(x(t),t)=9*x(t)-3*y(t)-6*t,diff(y(t),t)=-x(t)+11*y(t)+10*t],singsol=all)
\begin{align*} x \left (t \right ) &= c_{2} {\mathrm e}^{8 t}+{\mathrm e}^{12 t} c_{1} +\frac {3 t}{8}+\frac {1}{64} \\ y \left (t \right ) &= \frac {c_{2} {\mathrm e}^{8 t}}{3}-{\mathrm e}^{12 t} c_{1} -\frac {5}{64}-\frac {7 t}{8} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.113 (sec). Leaf size: 78
DSolve[{x'[t]==9*x[t]-3*y[t]-6*t,y'[t]==-x[t]+11*y[t]+10*t},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{64} \left (24 t+16 (c_1-3 c_2) e^{12 t}+48 (c_1+c_2) e^{8 t}+1\right ) \\ y(t)\to \frac {1}{64} \left (-56 t-16 (c_1-3 c_2) e^{12 t}+16 (c_1+c_2) e^{8 t}-5\right ) \\ \end{align*}