Internal problem ID [6521]
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 }\left (t \right )&=4 x \left (t \right )-2 y \left (t \right )\\ y^{\prime }\left (t \right )&=5 x \left (t \right )+2 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (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)],singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{3 t} \left (c_{1} \sin \left (3 t \right )+c_{2} \cos \left (3 t \right )\right ) \\ y \left (t \right ) &= \frac {{\mathrm e}^{3 t} \left (c_{1} \sin \left (3 t \right )+3 c_{2} \sin \left (3 t \right )-3 c_{1} \cos \left (3 t \right )+c_{2} \cos \left (3 t \right )\right )}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.006 (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*}