Internal problem ID [14100]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number: 77.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=4 y \left (t \right )\\ y^{\prime }\left (t \right )&=-x \left (t \right )-2 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 76
dsolve([diff(x(t),t)=4*y(t),diff(y(t),t)=-x(t)-2*y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{-t} \left (\sin \left (\sqrt {3}\, t \right ) c_{1} +\cos \left (\sqrt {3}\, t \right ) c_{2} \right ) \\ y \left (t \right ) &= -\frac {{\mathrm e}^{-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 )}{4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 93
DSolve[{x'[t]==4*y[t],y'[t]==-x[t]-2*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{3} e^{-t} \left (3 c_1 \cos \left (\sqrt {3} t\right )+\sqrt {3} (c_1+4 c_2) \sin \left (\sqrt {3} t\right )\right ) \\ y(t)\to \frac {1}{3} e^{-t} \left (3 c_2 \cos \left (\sqrt {3} t\right )-\sqrt {3} (c_1+c_2) \sin \left (\sqrt {3} t\right )\right ) \\ \end{align*}