```python
from sympy import *
from sympy.abc import x
init_printing(use_unicode=True)

```


```python
F, m, a, = symbols("F m a")

newtons_2_law = Eq(F, m*a) 

display(newtons_2_law)
```


```python
f  = Function("f")(x)
f_ = Derivative(f, x)
f_
```


```python
C = symbols("C")
Eq(ln(abs(y)), (-x**2/2+C))
```


```python
f = Function("f")(x)
g = Function("g")(x)
y_ = Derivative(y, x)
eq1 = Eq(y_, f*g)
display(eq1)
```


```python
(1/-y).diff(y)
```


```python
t, lam = symbols('t lambda')
y = Function('y')(t)
dydt = y.diff(t)
expr = Eq(dydt, -lam*y)
display(expr)
dsolve(expr)
```


```python
# eq4 = Eq(Derivative(y), 4*x*y)
# display(eq4)
# dsolve(eq4)

```


```python
y = Function('y')(x)
dydx = y.diff(x)
eq3 = Eq(dydx, y)
display(eq3)
dsolve(eq3)
```


```python
y = Function('y')
der = Derivative(y, x)
der
```


```python
0
```


```python

```

8d855efd8697e578b0a6f8aced1edf052ba0f280
ipynb
Jupyter Notebook
differential_equations/lab.ipynb
beltrewilton/mitx_18.01.2x
5b3b260b9ef979b17d28465824e98a5138a9e8b6
MIT
differential_equations/lab.ipynb
beltrewilton/mitx_18.01.2x
5b3b260b9ef979b17d28465824e98a5138a9e8b6
MIT
differential_equations/lab.ipynb
beltrewilton/mitx_18.01.2x
5b3b260b9ef979b17d28465824e98a5138a9e8b6
MIT
Qwen/Qwen-72B
1. YES
2. YES