Internal problem ID [11030]
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 \left (t \right )+18 \,{\mathrm e}^{t}\\ y^{\prime }\left (t \right )&=-10 x \left (t \right )+9 y \left (t \right )+37 \end {align*}
✓ Solution by Maple
Time used: 0.047 (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],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = 10+\frac {{\mathrm e}^{t} \left (3 \sin \left (6 t \right ) c_{1} +4 \sin \left (6 t \right ) c_{2} +4 \cos \left (6 t \right ) c_{1} -3 \cos \left (6 t \right ) c_{2} -15 \sin \left (6 t \right )-20 \cos \left (6 t \right )-20\right )}{5} \] \[ y \left (t \right ) = 7+{\mathrm e}^{t} \left (\sin \left (6 t \right ) c_{2} +\cos \left (6 t \right ) c_{1} -5 \cos \left (6 t \right )-5\right ) \]
✓ Solution by Mathematica
Time used: 0.407 (sec). Leaf size: 74
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 10+\frac {1}{3} e^t (3 c_1 \cos (6 t)+(5 c_2-4 c_1) \sin (6 t)-12) \\ y(t)\to 7+\frac {1}{3} e^t (3 c_2 \cos (6 t)+(4 c_2-5 c_1) \sin (6 t)-15) \\ \end{align*}