Internal problem ID [272]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 7.2, Matrices and Linear systems. Page 417
Problem number: problem 3.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }&=-3 y \left (t \right )\\ y^{\prime }\left (t \right )&=3 x \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 35
dsolve([diff(x(t),t)=-3*y(t),diff(y(t),t)=3*x(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = c_{1} \cos \left (3 t \right )-c_{2} \sin \left (3 t \right ) \] \[ y \left (t \right ) = c_{1} \sin \left (3 t \right )+c_{2} \cos \left (3 t \right ) \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 68
DSolve[{x'[t]==3*y[t],y'[t]==3*x[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{2} e^{-3 t} \left (c_1 \left (e^{6 t}+1\right )+c_2 \left (e^{6 t}-1\right )\right ) y(t)\to \frac {1}{2} e^{-3 t} \left (c_1 \left (e^{6 t}-1\right )+c_2 \left (e^{6 t}+1\right )\right ) \end{align*}