```python
from sympy import *
```


```python
x = Symbol('x')
y = Function('y')
ec = Eq(x**2*y(x).diff(x,2) - 3*x*y(x).diff(x) + 6*y(x),0)
```


```python
ec
```




$\displaystyle x^{2} \frac{d^{2}}{d x^{2}} y{\left(x \right)} - 3 x \frac{d}{d x} y{\left(x \right)} + 6 y{\left(x \right)} = 0$




```python
print('Ejercicio a ')
dsolve(ec)
```

    Ejercicio a 





$\displaystyle y{\left(x \right)} = C_{2} e^{- 2 x} + \left(C_{1} + 2 x\right) e^{2 x}$




```python

ec = Eq(x**2*y(x).diff(x,2) + 5*x*y(x).diff(x) + 4*y(x),0)
```


```python
print('ejrcicio b')
ec = Eq(x**2*y(x).diff(x,2) + 5*x*y(x).diff(x) + 4*y(x),0)
dsolve(ec)
```

    ejrcicio b





$\displaystyle y{\left(x \right)} = \frac{C_{1} + C_{2} \log{\left(x \right)}}{x^{2}}$




```python
ec = Eq(x**2*y(x).diff(x,2) + 9*x*y(x).diff(x) +17*y(x),0)
print('Ejercicio C')
dsolve(ec)
```

    Ejercicio C





$\displaystyle y{\left(x \right)} = \frac{C_{1} \sin{\left(\log{\left(x \right)} \right)} + C_{2} \cos{\left(\log{\left(x \right)} \right)}}{x^{4}}$




```python
print('Ejercicio d')
ec = Eq(y(x).diff(x,2) - 4*y(x),8*exp(2*x))
ec
```

    Ejercicio d





$\displaystyle - 4 y{\left(x \right)} + \frac{d^{2}}{d x^{2}} y{\left(x \right)} = 8 e^{2 x}$




```python
dsolve(ec)
```




$\displaystyle y{\left(x \right)} = C_{2} e^{- 2 x} + \left(C_{1} + 2 x\right) e^{2 x}$




```python
print(' Ejercicio e ')
ec = Eq(y(x).diff(x,2)-4*y(x).diff(x)+ 4*y(x),exp(-2*x))
dsolve(ec)
```

     Ejercicio e 





$\displaystyle y{\left(x \right)} = \left(C_{1} + C_{2} x\right) e^{2 x} + \frac{e^{- 2 x}}{16}$




```python

```

9d03d4068c79759f8f5f7138180603bb579be148
ipynb
Jupyter Notebook
talllerprogramacion.ipynb
sergiorodri234/sergiorodri234.github.io
311597033b7ce94aaa8dcf85c34461ffdc7aa661
MIT
talllerprogramacion.ipynb
sergiorodri234/sergiorodri234.github.io
311597033b7ce94aaa8dcf85c34461ffdc7aa661
MIT
talllerprogramacion.ipynb
sergiorodri234/sergiorodri234.github.io
311597033b7ce94aaa8dcf85c34461ffdc7aa661
MIT
2022-02-24T20:47:09.000Z
2022-02-24T20:47:09.000Z
Qwen/Qwen-72B
1. YES
2. YES