Internal problem ID [14924]
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: 7.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }&=-3 x+6 y \left (t \right )\\ y^{\prime }\left (t \right )&=4 x-y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 35
dsolve([diff(x(t),t)=-3*x(t)+6*y(t),diff(y(t),t)=4*x(t)-y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{-7 t}+c_{2} {\mathrm e}^{3 t} \\ y \left (t \right ) &= -\frac {2 c_{1} {\mathrm e}^{-7 t}}{3}+c_{2} {\mathrm e}^{3 t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 74
DSolve[{x'[t]==-3*x[t]+6*y[t],y'[t]==4*x[t]-y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{5} e^{-7 t} \left (c_1 \left (2 e^{10 t}+3\right )+3 c_2 \left (e^{10 t}-1\right )\right ) \\ y(t)\to \frac {1}{5} e^{-7 t} \left (2 c_1 \left (e^{10 t}-1\right )+c_2 \left (3 e^{10 t}+2\right )\right ) \\ \end{align*}