Internal problem ID [11045]
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 \left (t \right )-6 t\\ y^{\prime }\left (t \right )&=-x \left (t \right )+11 y \left (t \right )+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],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = 3 \,{\mathrm e}^{8 t} c_{2} -{\mathrm e}^{12 t} c_{1} +\frac {1}{64}+\frac {3 t}{8} \] \[ y \left (t \right ) = {\mathrm e}^{8 t} c_{2} +{\mathrm e}^{12 t} c_{1} -\frac {7 t}{8}-\frac {5}{64} \]
✓ Solution by Mathematica
Time used: 0.074 (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 e^{8 t} \left (-(c_1-3 c_2) e^{4 t}+c_1+c_2\right )-5\right ) \\ \end{align*}