Internal problem ID [7041]
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 }\left (t \right )&=-2 x \left (t \right )+3 y \left (t \right )\\ y^{\prime }\left (t \right )&=-2 x \left (t \right )+5 y \left (t \right ) \end {align*}
With initial conditions \[ [x \left (0\right ) = -2, y \left (0\right ) = 1] \]
✓ Solution by Maple
Time used: 0.0 (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], 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: 0.007 (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*}