Internal problem ID [13138]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 3. Linear Systems. Exercises section 3.8 page 371
Problem number: 15.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=y\\ y^{\prime }&=z \left (t \right )\\ z^{\prime }\left (t \right )&=0 \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 28
dsolve([diff(x(t),t)=0*x(t)+1*y(t)+0*z(t),diff(y(t),t)=0*x(t)+0*y(t)+1*z(t),diff(z(t),t)=0*x(t)+0*y(t)+0*z(t)],singsol=all)
\begin{align*} x \left (t \right ) &= \frac {1}{2} c_{3} t^{2}+c_{2} t +c_{1} \\ y \left (t \right ) &= c_{3} t +c_{2} \\ z \left (t \right ) &= c_{3} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 36
DSolve[{x'[t]==0*x[t]+1*y[t]+0*z[t],y'[t]==0*x[t]+0*y[t]+1*z[t],z'[t]==0*x[t]+0*y[t]+0*z[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {c_3 t^2}{2}+c_2 t+c_1 \\ y(t)\to c_3 t+c_2 \\ z(t)\to c_3 \\ \end{align*}