Internal problem ID [12386]
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(c).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=7 x \left (t \right )-4 y+10 \,{\mathrm e}^{t}\\ y^{\prime }&=3 x \left (t \right )+14 y+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: 54
dsolve([diff(x(t),t) = 7*x(t)-4*y(t)+10*exp(t), diff(y(t),t) = 3*x(t)+14*y(t)+6*exp(2*t), x(0) = 1, y(0) = -1], singsol=all)
\begin{align*} x \left (t \right ) &= -\frac {14 \,{\mathrm e}^{11 t}}{3}+\frac {67 \,{\mathrm e}^{10 t}}{9}-\frac {{\mathrm e}^{2 t}}{3}-\frac {13 \,{\mathrm e}^{t}}{9} \\ y \left (t \right ) &= \frac {14 \,{\mathrm e}^{11 t}}{3}-\frac {67 \,{\mathrm e}^{10 t}}{12}-\frac {5 \,{\mathrm e}^{2 t}}{12}+\frac {{\mathrm e}^{t}}{3} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 54
DSolve[{x'[t]==7*x[t]-4*y[t]+10*Exp[t],y'[t]==3*x[t]+14*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}{9} e^t \left (-40 e^{9 t}+18 e^{10 t}+13\right ) \\ y(t)\to \frac {1}{3} e^t \left (-10 e^{9 t}+6 e^{10 t}+1\right ) \\ \end{align*}