55.1.14 problem HW 5 problem 6

Internal problem ID [8710]
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 6
Date solved : Monday, January 27, 2025 at 04:20:01 PM
CAS classification : system_of_ODEs

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

With initial conditions

\begin{align*} x \left (0\right ) = 3\\ y \left (0\right ) = 0 \end{align*}

✓ Solution by Maple

Time used: 0.021 (sec). Leaf size: 25

dsolve([diff(x(t),t) = -x(t)+4*y(t), diff(y(t),t) = 2*x(t)-3*y(t), x(0) = 3, y(0) = 0], singsol=all)
 

\begin{align*} x \left (t \right ) &= {\mathrm e}^{-5 t}+2 \,{\mathrm e}^{t} \\ y \left (t \right ) &= -{\mathrm e}^{-5 t}+{\mathrm e}^{t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 30

DSolve[{D[x[t],t]==-x[t]+4*y[t],D[y[t],t]==2*x[t]-3*y[t]},{x[0]==3,y[0]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to e^{-5 t}+2 e^t \\ y(t)\to e^t-e^{-5 t} \\ \end{align*}