Internal problem ID [12378]
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 3(c).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-7 x \left (t \right )+10 y+18 \,{\mathrm e}^{t}\\ y^{\prime }&=-10 x \left (t \right )+9 y+37 \end {align*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 81
dsolve([diff(x(t),t)=-7*x(t)+10*y(t)+18*exp(t),diff(y(t),t)=-10*x(t)+9*y(t)+37],singsol=all)
\begin{align*} x \left (t \right ) &= 10+\frac {{\mathrm e}^{t} \left (-20+3 \sin \left (6 t \right ) c_{1} +4 \sin \left (6 t \right ) c_{2} +4 \cos \left (6 t \right ) c_{1} -3 \cos \left (6 t \right ) c_{2} -15 \sin \left (6 t \right )-20 \cos \left (6 t \right )\right )}{5} \\ y \left (t \right ) &= 7+{\mathrm e}^{t} \left (-5+\sin \left (6 t \right ) c_{2} +\cos \left (6 t \right ) c_{1} -5 \cos \left (6 t \right )\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.622 (sec). Leaf size: 82
DSolve[{x'[t]==-7*x[t]+10*y[t]+18*Exp[t],y'[t]==-10*x[t]+9*y[t]+37},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -4 e^t+c_1 e^t \cos (6 t)-\frac {1}{3} (4 c_1-5 c_2) e^t \sin (6 t)+10 \\ y(t)\to -5 e^t+c_2 e^t \cos (6 t)-\frac {1}{3} (5 c_1-4 c_2) e^t \sin (6 t)+7 \\ \end{align*}