74.22.7 problem 7

Internal problem ID [16654]
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
Date solved : Tuesday, January 28, 2025 at 09:16:17 AM
CAS classification : system_of_ODEs

\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: 0.047 (sec). Leaf size: 34

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}^{3 t}+c_{2} {\mathrm e}^{-7 t} \\ y &= c_{1} {\mathrm e}^{3 t}-\frac {2 c_{2} {\mathrm e}^{-7 t}}{3} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 74

DSolve[{D[x[t],t]==-3*x[t]+6*y[t],D[y[t],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*}