Internal problem ID [6517]
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 10.2 Linear Systems. Page
380
Problem number: 3(c).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=x \left (t \right )+2 y \left (t \right )+t -1\\ y^{\prime }\left (t \right )&=3 x \left (t \right )+2 y \left (t \right )-5 t -2 \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 44
dsolve([diff(x(t),t)=x(t)+2*y(t)+t-1,diff(y(t),t)=3*x(t)+2*y(t)-5*t-2],singsol=all)
\begin{align*} x \left (t \right ) &= c_{2} {\mathrm e}^{4 t}+{\mathrm e}^{-t} c_{1} +3 t -2 \\ y \left (t \right ) &= \frac {3 c_{2} {\mathrm e}^{4 t}}{2}-{\mathrm e}^{-t} c_{1} +3-2 t \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.188 (sec). Leaf size: 88
DSolve[{x'[t]==x[t]+2*y[t]+t-1,y'[t]==3*x[t]+2*y[t]-5*t-2},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{5} e^{-t} \left (5 e^t (3 t-2)+2 (c_1+c_2) e^{5 t}+3 c_1-2 c_2\right ) \\ y(t)\to \frac {1}{5} e^{-t} \left (-5 e^t (2 t-3)+3 (c_1+c_2) e^{5 t}-3 c_1+2 c_2\right ) \\ \end{align*}