50.27.5 problem 5

Internal problem ID [8186]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 10. Systems of First-Order Equations. Section 10.2 Linear Systems. Page 380
Problem number : 5
Date solved : Monday, January 27, 2025 at 03:45:33 PM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.092 (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*}