Internal problem ID [11031]
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(d).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-14 x \left (t \right )+39 y \left (t \right )+78 \sinh \left (t \right )\\ y^{\prime }\left (t \right )&=-6 x \left (t \right )+16 y \left (t \right )+6 \cosh \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.329 (sec). Leaf size: 84
dsolve([diff(x(t),t)=-14*x(t)+39*y(t)+78*sinh(t),diff(y(t),t)=-6*x(t)+16*y(t)+6*cosh(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = \frac {5 \,{\mathrm e}^{t} \sin \left (3 t \right ) c_{2}}{2}-\frac {{\mathrm e}^{t} \cos \left (3 t \right ) c_{2}}{2}+\frac {5 \,{\mathrm e}^{t} \cos \left (3 t \right ) c_{1}}{2}+\frac {{\mathrm e}^{t} \sin \left (3 t \right ) c_{1}}{2}+\frac {119 \,{\mathrm e}^{-t}}{2}-\frac {105 \,{\mathrm e}^{t}}{2}+\cosh \left (t \right ) \] \[ y \left (t \right ) = {\mathrm e}^{t} \sin \left (3 t \right ) c_{2} +{\mathrm e}^{t} \cos \left (3 t \right ) c_{1} +21 \,{\mathrm e}^{-t}-21 \,{\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.415 (sec). Leaf size: 74
DSolve[{x'[t]==-14*x[t]+39*y[t]+78*Sinh[t],y'[t]==-6*x[t]+16*y[t]+6*Cosh[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -112 \sinh (t)+8 \cosh (t)+e^t (c_1 \cos (3 t)+(13 c_2-5 c_1) \sin (3 t)) \\ y(t)\to -42 \sinh (t)+e^t (c_2 \cos (3 t)+(5 c_2-2 c_1) \sin (3 t)) \\ \end{align*}