Internal problem ID [6528]
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 }\left (t \right )&=x \left (t \right )+y \left (t \right )-5 t +2\\ y^{\prime }\left (t \right )&=4 x \left (t \right )-2 y \left (t \right )-8 t -8 \end {align*}
✓ Solution by Maple
Time used: 0.047 (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)
\[ x \left (t \right ) = -\frac {c_{2} {\mathrm e}^{-3 t}}{4}+c_{1} {\mathrm e}^{2 t}+2+3 t \] \[ y \left (t \right ) = c_{2} {\mathrm e}^{-3 t}+c_{1} {\mathrm e}^{2 t}+2 t -1 \]
✓ Solution by Mathematica
Time used: 0.15 (sec). Leaf size: 92
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 \frac {1}{5} e^{-3 t} \left (5 e^{3 t} (3 t+2)+(4 c_1+c_2) e^{5 t}+c_1-c_2\right ) y(t)\to \frac {1}{5} e^{-3 t} \left (5 e^{3 t} (2 t-1)+(4 c_1+c_2) e^{5 t}-4 c_1+4 c_2\right ) \end{align*}