64.24.2 problem 2

Internal problem ID [13687]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 13, Nonlinear differential equations. Section 13.2, Exercises page 656
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 05:55:16 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=3 x \left (t \right )+2 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=x \left (t \right )+2 y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.037 (sec). Leaf size: 31

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

\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{t}+c_{2} {\mathrm e}^{4 t} \\ y \left (t \right ) &= -c_{1} {\mathrm e}^{t}+\frac {c_{2} {\mathrm e}^{4 t}}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 67

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

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