Internal problem ID [5447]
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: 13.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )&=x \left (t \right )-3 y \left (t \right )-1+{\mathrm e}^{-t}\\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )&=-2 x \left (t \right )-3 y \left (t \right )+{\mathrm e}^{2 t}+1 \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 42
dsolve([diff(x(t),t)-x(t)+diff(y(t),t)+3*y(t)=exp(-t)-1,diff(x(t),t)+2*x(t)+diff(y(t),t)+3*y(t)=exp(2*t)+1],[x(t), y(t)], singsol=all)
\begin{align*} x \left (t \right ) = \frac {{\mathrm e}^{2 t}}{3}+\frac {2}{3}-\frac {{\mathrm e}^{-t}}{3} y \left (t \right ) = -\frac {1}{9}-\frac {{\mathrm e}^{2 t}}{15}+\frac {{\mathrm e}^{-t}}{6}+{\mathrm e}^{-3 t} c_{1} \end{align*}
✓ Solution by Mathematica
Time used: 0.059 (sec). Leaf size: 62
DSolve[{x'[t]-x[t]+y'[t]+3*y[t]==Exp[-t]-1,x'[t]+2*x[t]+y'[t]+3*y[t]==Exp[2*t]+1},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{3} e^{-t} \left (2 e^t+e^{3 t}-1\right ) y(t)\to \frac {e^{-t}}{6}-\frac {e^{2 t}}{15}+\frac {1}{16} c_1 e^{-3 t}-\frac {1}{9} \end{align*}