Internal problem ID [5768]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 10. Systems of First-Order Equations. Section 10.3 Homogeneous Linear Systems
with Constant Coefficients. Page 387
Problem number: 1(b).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=4 x \relax (t )-2 y \relax (t )\\ y^{\prime }\relax (t )&=5 x \relax (t )+2 y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.093 (sec). Leaf size: 59
dsolve([diff(x(t),t)=4*x(t)-2*y(t),diff(y(t),t)=5*x(t)+2*y(t)],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = \frac {{\mathrm e}^{3 t} \left (\sin \left (3 t \right ) c_{1}-3 \sin \left (3 t \right ) c_{2}+3 \cos \left (3 t \right ) c_{1}+\cos \left (3 t \right ) c_{2}\right )}{5} \] \[ y \relax (t ) = {\mathrm e}^{3 t} \left (\sin \left (3 t \right ) c_{1}+\cos \left (3 t \right ) c_{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 70
DSolve[{x'[t]==4*x[t]-2*y[t],y'[t]==5*x[t]+2*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{3} e^{3 t} (3 c_1 \cos (3 t)+(c_1-2 c_2) \sin (3 t)) \\ y(t)\to \frac {1}{3} e^{3 t} (3 c_2 \cos (3 t)+(5 c_1-c_2) \sin (3 t)) \\ \end{align*}