78.27.4 problem 8

Internal problem ID [18469]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 10. Systems of First Order Equations. Section 55. Linear systems. Problems at page 496
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 11:50:31 AM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.049 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 25

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

\begin{align*} x(t)\to e^t (c_2 t+c_1) \\ y(t)\to c_2 e^t \\ \end{align*}