Internal problem ID [6540]
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 A. Drill exercises. Page
400
Problem number: 4(b).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-2 x \left (t \right )+y \left (t \right )-t +3\\ y^{\prime }\left (t \right )&=x \left (t \right )+4 y \left (t \right )+t -2 \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 90
dsolve([diff(x(t),t)=-2*x(t)+y(t)-t+3,diff(y(t),t)=x(t)+4*y(t)+t-2],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = {\mathrm e}^{\left (1+\sqrt {10}\right ) t} c_{2} \sqrt {10}-{\mathrm e}^{-\left (-1+\sqrt {10}\right ) t} c_{1} \sqrt {10}-3 \,{\mathrm e}^{\left (1+\sqrt {10}\right ) t} c_{2} -3 \,{\mathrm e}^{-\left (-1+\sqrt {10}\right ) t} c_{1} -\frac {5 t}{9}+\frac {145}{81} \] \[ y \left (t \right ) = {\mathrm e}^{\left (1+\sqrt {10}\right ) t} c_{2} +{\mathrm e}^{-\left (-1+\sqrt {10}\right ) t} c_{1} -\frac {t}{9}+\frac {2}{81} \]
✓ Solution by Mathematica
Time used: 10.617 (sec). Leaf size: 190
DSolve[{x'[t]==-2*x[t]+y[t]-t+3,y'[t]==x[t]+4*y[t]+t-2},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -\frac {e^{t-\sqrt {10} t} \left (100 e^{\left (\sqrt {10}-1\right ) t} (9 t-29)+81 \left (\left (3 \sqrt {10}-10\right ) c_1-\sqrt {10} c_2\right ) e^{2 \sqrt {10} t}-81 \left (10+3 \sqrt {10}\right ) c_1+81 \sqrt {10} c_2\right )}{1620} y(t)\to \frac {e^{t-\sqrt {10} t} \left (-20 e^{\left (\sqrt {10}-1\right ) t} (9 t-2)+81 \left (\sqrt {10} c_1+\left (10+3 \sqrt {10}\right ) c_2\right ) e^{2 \sqrt {10} t}-81 \left (\sqrt {10} c_1+\left (3 \sqrt {10}-10\right ) c_2\right )\right )}{1620} \end{align*}