Internal problem ID [15546]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 3 (Systems of differential equations). Section 23.2 The method of undetermined
coefficients. Exercises page 239
Problem number: 823.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=2 x \left (t \right )+y \left (t \right )-2 z \left (t \right )+2-t\\ y^{\prime }\left (t \right )&=1-x \left (t \right )\\ z^{\prime }\left (t \right )&=x \left (t \right )+y \left (t \right )-z \left (t \right )+1-t \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 51
dsolve([diff(x(t),t)=2*x(t)+y(t)-2*z(t)+2-t,diff(y(t),t)=1-x(t),diff(z(t),t)=x(t)+y(t)-z(t)+1-t],singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} \sin \left (t \right )-c_{2} {\mathrm e}^{t}-c_{3} \cos \left (t \right ) \\ y \left (t \right ) &= t +c_{1} \cos \left (t \right )+c_{2} {\mathrm e}^{t}+c_{3} \sin \left (t \right ) \\ z \left (t \right ) &= 1+c_{1} \sin \left (t \right )-c_{3} \cos \left (t \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.129 (sec). Leaf size: 92
DSolve[{x'[t]==2*x[t]+y[t]-2*z[t]+2-t,y'[t]==1-x[t],z'[t]==x[t]+y[t]-z[t]+1-t},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to (c_1-c_3) e^t+c_3 \cos (t)+(c_1+c_2-c_3) \sin (t) \\ y(t)\to t-c_1 e^t+c_3 e^t+(c_1+c_2-c_3) \cos (t)-c_3 \sin (t) \\ z(t)\to c_3 \cos (t)+(c_1+c_2-c_3) \sin (t)+1 \\ \end{align*}