AI Tutor
Back to Modeling with Systems

Exercise 1

Avg difficulty 2.5

Verify whether or not the given pair of functions, (x(t),y(t))(x(t), y(t)) form a solution to the system dxdt=4x+2ydydt=3x−y\begin{aligned} \frac{dx}{dt} & = 4x + 2y \\ \frac{dy}{dt} & = 3x - y \end{aligned}

  1. x(t)=e−2t+2e5tx(t) = e^{-2t} + 2e^{5t}, y(t)=−3e−2t+e5ty(t) = -3e^{-2t} + e^{5t}

  2. x(t)=2e−2tx(t) = 2e^{-2t}, y(t)=−6e−2ty(t) = -6 e^{-2t}

  3. x(t)=2e−2tx(t) = 2e^{-2t}, y(t)=−5e−2ty(t) = -5 e^{-2t}

  4. x(t)=c1e−2t+2c2e5tx(t) = c_1e^{-2t} + 2c_2e^{5t}, y(t)=−3c1e−2t+c2e5ty(t) = -3c_1 e^{-2t} + c_2 e^{5t}

Judson, The ODE Project, §2.1 Modeling with Systems, Exercise 1

AI Tutor

Adapted from The ODE Project © 2019–2025 Thomas W. Judson. Licensed under CC BY 4.0. Source: The ODE Project. Imported at revision 7935458.