64.16.4 problem 4

Internal problem ID [13607]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 7, Systems of linear differential equations. Section 7.1. Exercises page 277
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 05:53:48 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )+\frac {d}{d t}y \left (t \right )-x \left (t \right )-2 y \left (t \right )&=2 \,{\mathrm e}^{t}\\ \frac {d}{d t}x \left (t \right )+\frac {d}{d t}y \left (t \right )-3 x \left (t \right )-4 y \left (t \right )&={\mathrm e}^{2 t} \end{align*}

✓ Solution by Maple

Time used: 0.038 (sec). Leaf size: 22

dsolve([diff(x(t),t)+diff(y(t),t)-x(t)-2*y(t)=2*exp(t),diff(x(t),t)+diff(y(t),t)-3*x(t)-4*y(t)=exp(2*t)],singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 25

DSolve[{D[x[t],t]+D[y[t],t]-x[t]-2*y[t]==2*Exp[t],D[x[t],t]+D[y[t],t]-3*x[t]-4*y[t]==Exp[2*t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to 3 e^t \\ y(t)\to -\frac {1}{2} e^t \left (e^t+4\right ) \\ \end{align*}