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 }\relax (t )&=-3 y \relax (t )\\ y^{\prime }\relax (t )&=3 x \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.058 (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)
\[ x \relax (t ) = c_{1} \cos \left (3 t \right )-c_{2} \sin \left (3 t \right ) \] \[ y \relax (t ) = c_{1} \sin \left (3 t \right )+c_{2} \cos \left (3 t \right ) \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 38
DSolve[{x'[t]==3*y[t],y'[t]==3*x[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 \cosh (3 t)+c_2 \sinh (3 t) \\ y(t)\to c_2 \cosh (3 t)+c_1 \sinh (3 t) \\ \end{align*}