72.14.11 problem 15

Internal problem ID [14874]
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
Date solved : Tuesday, January 28, 2025 at 07:17:59 AM
CAS classification : system_of_ODEs

\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: 0.069 (sec). Leaf size: 27

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 &= c_{3} t +c_{2} \\ z &= c_{3} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 36

DSolve[{D[x[t],t]==0*x[t]+1*y[t]+0*z[t],D[y[t],t]==0*x[t]+0*y[t]+1*z[t],D[z[t],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*}