Internal problem ID [6289]
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.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=-x \relax (t )+4 y \relax (t )\\ y^{\prime }\relax (t )&=2 x \relax (t )-3 y \relax (t ) \end {align*}
With initial conditions \[ [x \relax (0) = 3, y \relax (0) = 0] \]
✓ Solution by Maple
Time used: 0.064 (sec). Leaf size: 26
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],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = {\mathrm e}^{-5 t}+2 \,{\mathrm e}^{t} \] \[ y \relax (t ) = -{\mathrm e}^{-5 t}+{\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 30
DSolve[{x'[t]==-x[t]+4*y[t],y'[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*}