67.5.16 problem Problem 3(e)

Internal problem ID [14102]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 6. Introduction to Systems of ODEs. Problems page 408
Problem number : Problem 3(e)
Date solved : Tuesday, January 28, 2025 at 06:14:28 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )-3 x \left (t \right )+2 y&=0\\ y^{\prime }-x \left (t \right )+3 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.038 (sec). Leaf size: 70

dsolve([diff(x(t),t)-3*x(t)+2*y(t)=0,diff(y(t),t)-x(t)+3*y(t)=0],singsol=all)
 

\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{\sqrt {7}\, t}+c_{2} {\mathrm e}^{-\sqrt {7}\, t} \\ y &= -\frac {c_{1} \sqrt {7}\, {\mathrm e}^{\sqrt {7}\, t}}{2}+\frac {c_{2} \sqrt {7}\, {\mathrm e}^{-\sqrt {7}\, t}}{2}+\frac {3 c_{1} {\mathrm e}^{\sqrt {7}\, t}}{2}+\frac {3 c_{2} {\mathrm e}^{-\sqrt {7}\, t}}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 144

DSolve[{D[x[t],t]-3*x[t]+2*y[t]==0,D[y[t],t]-x[t]+3*y[t]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to \frac {1}{14} e^{-\sqrt {7} t} \left (c_1 \left (\left (7+3 \sqrt {7}\right ) e^{2 \sqrt {7} t}+7-3 \sqrt {7}\right )-2 \sqrt {7} c_2 \left (e^{2 \sqrt {7} t}-1\right )\right ) \\ y(t)\to \frac {1}{14} e^{-\sqrt {7} t} \left (\sqrt {7} c_1 \left (e^{2 \sqrt {7} t}-1\right )-c_2 \left (\left (3 \sqrt {7}-7\right ) e^{2 \sqrt {7} t}-7-3 \sqrt {7}\right )\right ) \\ \end{align*}