55.1.13 problem HW 5 problem 5

Internal problem ID [8709]
Book : Selected problems from homeworks from different courses
Section : Math 2520, summer 2021. Differential Equations and Linear Algebra. Normandale college, Bloomington, Minnesota
Problem number : HW 5 problem 5
Date solved : Monday, January 27, 2025 at 04:20:00 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=-2 x \left (t \right )+3 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=-2 x \left (t \right )+5 y \left (t \right ) \end{align*}

With initial conditions

\begin{align*} x \left (0\right ) = -2\\ y \left (0\right ) = 1 \end{align*}

✓ Solution by Maple

Time used: 0.025 (sec). Leaf size: 31

dsolve([diff(x(t),t) = -2*x(t)+3*y(t), diff(y(t),t) = -2*x(t)+5*y(t), x(0) = -2, y(0) = 1], singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 36

DSolve[{D[x[t],t]==-2*x[t]+3*y[t],D[y[t],t]==-2*x[t]+5*y[t]},{x[0]==-2,y[0]==1},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to e^{-t} \left (e^{5 t}-3\right ) \\ y(t)\to e^{-t} \left (2 e^{5 t}-1\right ) \\ \end{align*}