Internal problem ID [5764]
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 }\relax (t )&=x \relax (t )+2 y \relax (t )+t -1\\ y^{\prime }\relax (t )&=3 x \relax (t )+2 y \relax (t )-5 t -2 \end {align*}
✓ Solution by Maple
Time used: 0.058 (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],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = -c_{2} {\mathrm e}^{-t}+\frac {2 c_{1} {\mathrm e}^{4 t}}{3}-2+3 t \] \[ y \relax (t ) = c_{2} {\mathrm e}^{-t}+c_{1} {\mathrm e}^{4 t}-2 t +3 \]
✓ Solution by Mathematica
Time used: 0.112 (sec). Leaf size: 78
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 3 t+\frac {1}{5} e^{-t} \left (2 (c_1+c_2) e^{5 t}+3 c_1-2 c_2\right )-2 \\ y(t)\to -2 t+\frac {1}{5} e^{-t} \left (3 (c_1+c_2) e^{5 t}-3 c_1+2 c_2\right )+3 \\ \end{align*}