Internal problem ID [11044]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 8.4 Systems of Linear Differential Equations (Method of Undetermined Coefficients).
Problems page 520
Problem number: Problem 1(a).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=x \left (t \right )+5 y \left (t \right )+10 \sinh \left (t \right )\\ y^{\prime }\left (t \right )&=19 x \left (t \right )-13 y \left (t \right )+24 \sinh \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.219 (sec). Leaf size: 176
dsolve([diff(x(t),t)=x(t)+5*y(t)+10*sinh(t),diff(y(t),t)=19*x(t)-13*y(t)+24*sinh(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -\frac {71 \sinh \left (7 t \right ) {\mathrm e}^{6 t}}{266}-\frac {7 \cosh \left (5 t \right ) {\mathrm e}^{6 t}}{12}+\frac {71 \cosh \left (7 t \right ) {\mathrm e}^{6 t}}{266}+\frac {7 \sinh \left (5 t \right ) {\mathrm e}^{6 t}}{12}+\frac {71 \,{\mathrm e}^{-18 t} \cosh \left (17 t \right )}{646}-\frac {35 \,{\mathrm e}^{-18 t} \cosh \left (19 t \right )}{228}+\frac {71 \,{\mathrm e}^{-18 t} \sinh \left (17 t \right )}{646}-\frac {35 \,{\mathrm e}^{-18 t} \sinh \left (19 t \right )}{228}+c_{2} {\mathrm e}^{6 t}-\frac {5 c_{1} {\mathrm e}^{-18 t}}{19}-\frac {24 \sinh \left (t \right )}{19} \] \[ y \left (t \right ) = c_{2} {\mathrm e}^{6 t}+c_{1} {\mathrm e}^{-18 t}+\frac {71 \left (\left (-\frac {323 \cosh \left (5 t \right )}{71}+\frac {17 \cosh \left (7 t \right )}{7}+\frac {323 \sinh \left (5 t \right )}{71}-\frac {17 \sinh \left (7 t \right )}{7}\right ) {\mathrm e}^{24 t}+\sinh \left (17 t \right )-\frac {85 \sinh \left (19 t \right )}{71}+\cosh \left (17 t \right )-\frac {85 \cosh \left (19 t \right )}{71}\right ) {\mathrm e}^{-18 t}}{408} \]
✓ Solution by Mathematica
Time used: 0.046 (sec). Leaf size: 108
DSolve[{x'[t]==x[t]+5*y[t]+10*Sinh[t],y'[t]==19*x[t]-13*y[t]+24*Sinh[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {120 e^{-t}}{119}-\frac {26 e^t}{19}+\frac {5}{24} (c_1-c_2) e^{-18 t}+\frac {1}{24} (19 c_1+5 c_2) e^{6 t} \\ y(t)\to \frac {71 e^{-t}}{119}-e^t+\frac {19}{24} (c_2-c_1) e^{-18 t}+\frac {1}{24} (19 c_1+5 c_2) e^{6 t} \\ \end{align*}