Internal problem ID [11039]
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(d).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-7 x \left (t \right )+4 y \left (t \right )+6 \,{\mathrm e}^{3 t}\\ y^{\prime }\left (t \right )&=-5 x \left (t \right )+2 y \left (t \right )+6 \,{\mathrm e}^{2 t} \end {align*}
With initial conditions \[ [x \left (0\right ) = 1, y \left (0\right ) = -1] \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 58
dsolve([diff(x(t),t) = -7*x(t)+4*y(t)+6*exp(3*t), diff(y(t),t) = -5*x(t)+2*y(t)+6*exp(2*t), x(0) = 1, y(0) = -1],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = \frac {6 \,{\mathrm e}^{2 t}}{5}+\frac {44 \,{\mathrm e}^{-3 t}}{5}-\frac {46 \,{\mathrm e}^{-2 t}}{5}+\frac {{\mathrm e}^{3 t}}{5} \] \[ y \left (t \right ) = \frac {44 \,{\mathrm e}^{-3 t}}{5}-\frac {23 \,{\mathrm e}^{-2 t}}{2}+\frac {27 \,{\mathrm e}^{2 t}}{10}-{\mathrm e}^{3 t} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 48
DSolve[{x'[t]==-7*x[t]+4*y[t]+6*Exp[3*t],y'[t]==-5*x[t]+2*y[t]+6*Exp[2*t]},{x[0]==1,y[0]==-1},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{5} e^{-3 t} \left (-16 e^t+e^{6 t}+20\right ) \\ y(t)\to -e^{-3 t} \left (4 e^t+e^{6 t}-4\right ) \\ \end{align*}