Internal problem ID [11036]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 8.3 Systems of Linear Differential Equations (Variation of Parameters). Problems
page 514
Problem number: Problem 5(a).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=7 x \left (t \right )+y \left (t \right )-1-6 \,{\mathrm e}^{t}\\ y^{\prime }\left (t \right )&=-4 x \left (t \right )+3 y \left (t \right )+4 \,{\mathrm e}^{t}-3 \end {align*}
With initial conditions \[ [x \left (0\right ) = 1, y \left (0\right ) = -1] \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 30
dsolve([diff(x(t),t) = 7*x(t)+y(t)-1-6*exp(t), diff(y(t),t) = -4*x(t)+3*y(t)+4*exp(t)-3, x(0) = 1, y(0) = -1],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -2 t \,{\mathrm e}^{5 t}+{\mathrm e}^{t} \] \[ y \left (t \right ) = 1+\left (4 t -2\right ) {\mathrm e}^{5 t} \]
✓ Solution by Mathematica
Time used: 0.18 (sec). Leaf size: 51
DSolve[{x'[t]==7*x[t]+y[t]-1-Exp[t],y'[t]==-4*x[t]+3*y[t]+4*Exp[t]-3},{x[0]==1,y[0]==-1},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{8} e^t \left (e^{4 t} (4 t+5)+3\right ) \\ y(t)\to \frac {1}{4} \left (-e^{5 t} (4 t+3)-5 e^t+4\right ) \\ \end{align*}