Internal problem ID [5448]
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: 17.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=1+x \left (t \right )+\frac {{\mathrm e}^{t}}{2}\\ y^{\prime }\left (t \right )&=-2 y \left (t \right )+\frac {{\mathrm e}^{t}}{2}\\ z^{\prime }\left (t \right )&=2-z \left (t \right )+\frac {{\mathrm e}^{t}}{2} \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 45
dsolve([diff(x(t),t)-x(t)+diff(y(t),t)+2*y(t)=1+exp(t),diff(y(t),t)+2*y(t)+diff(z(t),t)+z(t)=2+exp(t),diff(x(t),t)-x(t)+diff(z(t),t)+z(t)=3+exp(t)],[x(t), y(t), z(t)], singsol=all)
\begin{align*} x \left (t \right ) = -1+\frac {{\mathrm e}^{t} \left (2 c_{1} +t \right )}{2} y \left (t \right ) = \frac {{\mathrm e}^{t}}{6}+{\mathrm e}^{-2 t} c_{2} z \left (t \right ) = 2+\frac {{\mathrm e}^{t}}{4}+{\mathrm e}^{-t} c_{3} \end{align*}
✓ Solution by Mathematica
Time used: 0.116 (sec). Leaf size: 60
DSolve[{x'[t]-x[t]+y'[t]+2*y[t]==1+Exp[t],y'[t]+2*y[t]+z'[t]+z[t]==2+Exp[t],x'[t]-x[t]+z'[t]+z[t]==3+Exp[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -1+e^t \left (\frac {t}{2}+c_1\right ) y(t)\to \frac {e^t}{6}+c_2 e^{-2 t} z(t)\to \frac {e^t}{4}+(4+c_3) e^{-t}+2 \end{align*}