Internal problem ID [273]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 7.2, Matrices and Linear systems. Page 417
Problem number: problem 4.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=3 x \relax (t )-2 y \relax (t )\\ y^{\prime }\relax (t )&=2 x \relax (t )+y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 78
dsolve([diff(x(t),t)=3*x(t)-2*y(t),diff(y(t),t)=2*x(t)+y(t)],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = -\frac {{\mathrm e}^{2 t} \left (\sqrt {3}\, \sin \left (\sqrt {3}\, t \right ) c_{2}-\sqrt {3}\, \cos \left (\sqrt {3}\, t \right ) c_{1}-\sin \left (\sqrt {3}\, t \right ) c_{1}-\cos \left (\sqrt {3}\, t \right ) c_{2}\right )}{2} \] \[ y \relax (t ) = {\mathrm e}^{2 t} \left (\sin \left (\sqrt {3}\, t \right ) c_{1}+\cos \left (\sqrt {3}\, t \right ) c_{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 96
DSolve[{x'[t]==3*x[t]-2*y[t],y'[t]==2*x[t]+y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{3} e^{2 t} \left (3 c_1 \cos \left (\sqrt {3} t\right )+\sqrt {3} (c_1-2 c_2) \sin \left (\sqrt {3} t\right )\right ) \\ y(t)\to \frac {1}{3} e^{2 t} \left (3 c_2 \cos \left (\sqrt {3} t\right )+\sqrt {3} (2 c_1-c_2) \sin \left (\sqrt {3} t\right )\right ) \\ \end{align*}