```python
from sympy import *
```


```python
init_session()
```

    IPython console for SymPy 1.0 (Python 2.7.12-64-bit) (ground types: gmpy)
    
    These commands were executed:
    >>> from __future__ import division
    >>> from sympy import *
    >>> x, y, z, t = symbols('x y z t')
    >>> k, m, n = symbols('k m n', integer=True)
    >>> f, g, h = symbols('f g h', cls=Function)
    >>> init_printing()
    
    Documentation can be found at http://docs.sympy.org/1.0/



```python
t, P, e_r, e_d, delta_e, rho_e, g_e, i_r, i_d, delta_i, rho_i, g_i, b = symbols('t P \\tau_{er} \\tau_{ed} \\delta_e \\rho_e \\bar{g}_e \\tau_{ir} \\tau_{id} \\delta_i \\rho_i \\bar{g}_i \\beta', positive=True, real=True)
```


```python
C = g_e*(P*(tau_i/(tau_i-1))*exp((t-delta_i)/i_r)*(1 - exp(-(t-delta_i)/(i_r*(1+(1/tau_i))))) - (tau_e/(tau_e-1))*exp(t/e_r)*(1 - exp(-t/(e_r*(1+(1/tau_e))))))
```


```python
C
```


```python
C_prime = diff(C,t)
```


```python
C_prime
```


```python
C_check = C_prime.subs({P:2, tau_i:10, tau_e:4, delta_i:1/g_e, i_r : 2.8, e_r: 5, t: 4})
```


```python
simplify(C_check)
```


```python
p = plot(C_check, (g_e,0,20))
#p = plot_implicit(C_prime, (t,0,10), (g_e,0,0.5))
```


```python
p.show()
```


```python
p.show()
```


```python

```

d86375b098688e500db9e7dc677ac71314833387
ipynb
Jupyter Notebook
model/Final_equation.ipynb
elifesciences-publications/linearity
777769212ac43d854d23d5b967c6323747c56c09
MIT
2019-04-22T17:07:37.000Z
2019-04-22T17:07:37.000Z
model/Final_equation.ipynb
elifesciences-publications/linearity
777769212ac43d854d23d5b967c6323747c56c09
MIT
model/Final_equation.ipynb
elifesciences-publications/linearity
777769212ac43d854d23d5b967c6323747c56c09
MIT
2019-04-25T13:10:24.000Z
2021-09-05T03:45:36.000Z
Qwen/Qwen-72B
1. YES
2. YES