what is wrong with my python code? I am trying to write a code to plot the direction field/phase portrait for a system of linear differential equations. The solution passes through (-2,-2) and the equations are x_1'=2x_1 - x_2 and x_2'=-x_1 + x_2 ```pythonimport matplotlib.pyplot as pltfrom scipy.integrate import odeintfrom numpy import linalg as LAimport numpy as npa=2b=-1c=-1d=1## Vector field functiondef vf(X, t): x_1prime = a*X[0] + b*X[1] x_2prime = c*X[0] + d*X[1] return [x_1prime, x_2prime]## Solution curvest0 = 0; tEnd = 10t = np.linspace(t0, tEnd, 50*(tEnd-t0))x_1_0 = [0, -2] # First initial conditionx_1 = odeint(vf, x_1_0, t)x_2_0 = [-0.2] # Second initial conditionx_2 = odeint(vf, x_2_0, t)## Generate the eigenvaluesB = np.array([[a, b], [c, d]])u, v = LA.eig(B)print('eigenvalues and eigenvectors')print(u)print(v)```### ExplanationThis code snippet is written in Python and uses various libraries to integrate and analyze linear differential equations. Here's a breakdown of the elements:1. **Imports:** - `matplotlib.pyplot` as `plt`: Used for plotting graphs (though not used in the provided code portion). - `scipy.integrate.odeint`: Used for integrating ordinary differential equations. - `numpy.linalg` as `LA`: Provides functions for linear algebra operations like finding eigenvalues. - `numpy`: A library for numerical operations in Python.2. **Parameters:** - Coefficients `a`, `b`, `c`, and `d` are defined, which will be used in the vector field function to define a system of differential equations.3. **Vector Field Function:** - `vf(X, t)`: Defines a vector field function for a system where: - \( x'_1 = a \cdot X[0] + b \cdot X[1] \) - \( x'_2 = c \cdot X[0] + d \cdot X[1] \) This returns these derivatives as a list.4

We have to write a python code for the differential equationpasses through

what is wrong with my python code? I am trying to write a code to plot the direction field/phase portrait for a system of linear differential equations. The solution passes through (-2,-2) and the equations are x_1'=2x_1 - x_2 and x_2'=-x_1 + x_2

what is wrong with my python code? I am trying to write a code to plot the direction field/phase portrait for a system of linear differential equations. The solution passes through (-2,-2) and the equations are x_1'=2x_1 - x_2 and x_2'=-x_1 + x_2

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

100%

```python
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from numpy import linalg as LA
import numpy as np

a=2
b=-1
c=-1
d=1

## Vector field function
def vf(X, t):
x_1prime = a*X[0] + b*X[1]
x_2prime = c*X[0] + d*X[1]
return [x_1prime, x_2prime]

## Solution curves
t0 = 0; tEnd = 10
t = np.linspace(t0, tEnd, 50*(tEnd-t0))

x_1_0 = [0, -2] # First initial condition
x_1 = odeint(vf, x_1_0, t)

x_2_0 = [-0.2] # Second initial condition
x_2 = odeint(vf, x_2_0, t)

## Generate the eigenvalues
B = np.array([[a, b], [c, d]])
u, v = LA.eig(B)
print('eigenvalues and eigenvectors')
print(u)
print(v)
```

### Explanation

This code snippet is written in Python and uses various libraries to integrate and analyze linear differential equations. Here's a breakdown of the elements:

1. **Imports:**
- `matplotlib.pyplot` as `plt`: Used for plotting graphs (though not used in the provided code portion).
- `scipy.integrate.odeint`: Used for integrating ordinary differential equations.
- `numpy.linalg` as `LA`: Provides functions for linear algebra operations like finding eigenvalues.
- `numpy`: A library for numerical operations in Python.

2. **Parameters:**
- Coefficients `a`, `b`, `c`, and `d` are defined, which will be used in the vector field function to define a system of differential equations.

3. **Vector Field Function:**
- `vf(X, t)`: Defines a vector field function for a system where:
- \( x'_1 = a \cdot X[0] + b \cdot X[1] \)
- \( x'_2 = c \cdot X[0] + d \cdot X[1] \)
This returns these derivatives as a list.

4

With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.

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