Internal problem ID [5775]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 10. Systems of First-Order Equations. Section 10.3 Homogeneous Linear Systems
with Constant Coefficients. Page 387
Problem number: 5(b).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=x \relax (t )+y \relax (t )-5 t +2\\ y^{\prime }\relax (t )&=4 x \relax (t )-2 y \relax (t )-8 t -8 \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 43
dsolve([diff(x(t),t)=x(t)+y(t)-5*t+2,diff(y(t),t)=4*x(t)-2*y(t)-8*t-8],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = c_{2} {\mathrm e}^{2 t}-\frac {c_{1} {\mathrm e}^{-3 t}}{4}+2+3 t \] \[ y \relax (t ) = c_{2} {\mathrm e}^{2 t}+c_{1} {\mathrm e}^{-3 t}+2 t -1 \]
✓ Solution by Mathematica
Time used: 0.18 (sec). Leaf size: 81
DSolve[{x'[t]==x[t]+y[t]-5*t+2,y'[t]==4*x[t]-2*y[t]-8*t-8},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to 3 t+\frac {1}{5} \left ((c_1-c_2) e^{-3 t}+(4 c_1+c_2) e^{2 t}+10\right ) \\ y(t)\to 2 t+\frac {1}{5} \left (-4 (c_1-c_2) e^{-3 t}+(4 c_1+c_2) e^{2 t}-5\right ) \\ \end{align*}