1.13 problem HW 5 problem 5

Internal problem ID [6288]

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.
ODE order: 1.
ODE degree: 1.

Solve \begin {align*} x^{\prime }\relax (t )&=-2 x \relax (t )+3 y \relax (t )\\ y^{\prime }\relax (t )&=-2 x \relax (t )+5 y \relax (t ) \end {align*}

With initial conditions \[ [x \relax (0) = -2, y \relax (0) = 1] \]

Solution by Maple

Time used: 0.109 (sec). Leaf size: 32

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],[x(t), y(t)], singsol=all)
 

\[ x \relax (t ) = -3 \,{\mathrm e}^{-t}+{\mathrm e}^{4 t} \] \[ y \relax (t ) = -{\mathrm e}^{-t}+2 \,{\mathrm e}^{4 t} \]

Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 36

DSolve[{x'[t]==-2*x[t]+3*y[t],y'[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*}