Internal problem ID [14927]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 6. Systems of Differential Equations. Exercises 6.1, page 282
Problem number: 10.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }&=4 x+2 y \left (t \right )\\ y^{\prime }\left (t \right )&=-x+2 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 46
dsolve([diff(x(t),t)=4*x(t)+2*y(t),diff(y(t),t)=-x(t)+2*y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{3 t} \left (c_{1} \sin \left (t \right )+c_{2} \cos \left (t \right )\right ) \\ y \left (t \right ) &= -\frac {{\mathrm e}^{3 t} \left (c_{1} \sin \left (t \right )+c_{2} \sin \left (t \right )-c_{1} \cos \left (t \right )+c_{2} \cos \left (t \right )\right )}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 51
DSolve[{x'[t]==4*x[t]+2*y[t],y'[t]==-x[t]+2*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{3 t} (c_1 \cos (t)+(c_1+2 c_2) \sin (t)) \\ y(t)\to e^{3 t} (c_2 \cos (t)-(c_1+c_2) \sin (t)) \\ \end{align*}