Internal problem ID [5446]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 21. System of simultaneous linear equations. Supplemetary problems. Page
163
Problem number: 12.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=4-5 x \left (t \right )-y \left (t \right )-{\mathrm e}^{t}\\ y^{\prime }\left (t \right )&=2 x \left (t \right )-3 y \left (t \right )+{\mathrm e}^{t}-1 \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 71
dsolve([diff(x(t),t)+x(t)+2*diff(y(t),t)+7*y(t)=exp(t)+2,-2*x(t)+diff(y(t),t)+3*y(t)=exp(t)-1],singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{-4 t} \sin \left (t \right ) c_{2} +{\mathrm e}^{-4 t} \cos \left (t \right ) c_{1} +\frac {13}{17}-\frac {5 \,{\mathrm e}^{t}}{26} \\ y \left (t \right ) &= -{\mathrm e}^{-4 t} \sin \left (t \right ) c_{2} -{\mathrm e}^{-4 t} \cos \left (t \right ) c_{2} -{\mathrm e}^{-4 t} \cos \left (t \right ) c_{1} +{\mathrm e}^{-4 t} \sin \left (t \right ) c_{1} +\frac {2 \,{\mathrm e}^{t}}{13}+\frac {3}{17} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.239 (sec). Leaf size: 79
DSolve[{x'[t]+x[t]+2*y'[t]+7*y[t]==Exp[t]+2,-2*x[t]+y'[t]+3*y[t]==Exp[t]-1},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -\frac {5 e^t}{26}+c_1 e^{-4 t} \cos (t)-(c_1+c_2) e^{-4 t} \sin (t)+\frac {13}{17} \\ y(t)\to \frac {2 e^t}{13}+c_2 e^{-4 t} \cos (t)+(2 c_1+c_2) e^{-4 t} \sin (t)+\frac {3}{17} \\ \end{align*}