2023-02-05 15:11:55 +0200 | received badge | ● Famous Question (source) |
2018-04-22 08:54:28 +0200 | received badge | ● Notable Question (source) |
2016-05-01 13:32:35 +0200 | received badge | ● Popular Question (source) |
2015-07-02 20:52:10 +0200 | asked a question | Solving system of ODEs I'm trying to solve a system of 4 ODEs using Sage. I'm able to get a solution, but it's not at all what I expect. Here are the 4 equations: $$\frac{dw}{dt} = \frac{Q_x}{V} x(t) - \frac{Q_y}{V}\eta w(t) - \frac{Q_z}{V} \eta w(t)$$ $$\frac{dx}{dt} = \frac{Q_y}{V} \gamma y(t) + \frac{Q_z}{V} \zeta z(t) - \frac{Q_x}{V}x(t)$$ $$\frac{dy}{dt} = \frac{Q_y}{V} \eta w(t) - \frac{Q_y}{V} \gamma y(t) $$ $$\frac{dz}{dt} = \frac{Q_z}{V} \eta w(t) - \frac{Q_z}{V} \zeta z(t)$$ Here is how I've coded the problem in Sage. Where m_0 is an initial mass that exists in the x volume at time 0. All other volumes are empty at time 0. I'm expecting relatively simple exponential equations as the solution, but what I get in return is some significantly more complex. $$ w\left(\mathit{time}\right) = \frac{V \gamma m_{0} \zeta}{{\left(\eta \gamma + {\left(\eta \gamma + \eta\right)} \zeta\right)} V + \gamma \zeta} + \mathcal{L}^{-1}\left(-\frac{V^{4} g_{2562}^{2} \gamma m_{0} \zeta + {\left(Q_{x} Q_{z} - Q_{z}^{2}\right)} V^{2} \gamma^{2} m_{0} \zeta^{2} - {\left(Q_{x} Q_{z} \eta m_{0} \zeta^{2} + {\left(Q_{x}^{2} - Q_{x} Q_{z}\right)} \eta \gamma^{2} m_{0}\right)} V^{3} - {\left({\left(Q_{x} \eta \gamma m_{0} + Q_{x} \eta m_{0} \zeta\right)} V^{4} - {\left({\left(Q_{x} - Q_{z}\right)} \gamma^{2} m_{0} \zeta + Q_{z} \gamma m_{0} \zeta^{2}\right)} V^{3}\right)} g_{2562}}{{\left(V^{3} g_{2562}^{3} + {\left(Q_{x} V^{3} \eta + {\left({\left(Q_{x} - Q_{z}\right)} \gamma + Q_{z} \zeta + Q_{x}\right)} V^{2}\right)} g_{2562}^{2} + {\left(Q_{x}^{2} Q_{z} - Q_{x} Q_{z}^{2}\right)} \gamma \zeta + {\left({\left(Q_{x}^{2} Q_{z} - Q_{x} Q_{z}^{2}\right)} \eta \gamma + {\left({\left(Q_{x}^{2} Q_{z} - Q_{x} Q_{z}^{2}\right)} \eta \gamma + {\left(Q_{x}^{2} Q_{z} - Q_{x} Q_{z}^{2}\right)} \eta\right)} \zeta\right)} V + {\left({\left(Q_{x} Q_{z ... (more) |