Internal problem ID [13129]
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: 4.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=y\\ y^{\prime }&=-x \left (t \right )\\ z^{\prime }\left (t \right )&=2 z \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 36
dsolve([diff(x(t),t)=0*x(t)+1*y(t)+0*z(t),diff(y(t),t)=-1*x(t)+0*y(t)+0*z(t),diff(z(t),t)=0*x(t)+0*y(t)+2*z(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} \sin \left (t \right )+c_{2} \cos \left (t \right ) \\ y \left (t \right ) &= c_{1} \cos \left (t \right )-c_{2} \sin \left (t \right ) \\ z \left (t \right ) &= c_{3} {\mathrm e}^{2 t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.035 (sec). Leaf size: 76
DSolve[{x'[t]==0*x[t]+1*y[t]+0*z[t],y'[t]==-1*x[t]+0*y[t]+0*z[t],z'[t]==0*x[t]+0*y[t]+2*z[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 \cos (t)+c_2 \sin (t) \\ y(t)\to c_2 \cos (t)-c_1 \sin (t) \\ z(t)\to c_3 e^{2 t} \\ x(t)\to c_1 \cos (t)+c_2 \sin (t) \\ y(t)\to c_2 \cos (t)-c_1 \sin (t) \\ z(t)\to 0 \\ \end{align*}