#### Euler Method

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```from collections.abc import Callable

import numpy as np

def explicit_euler(
ode_func: Callable, y0: float, x0: float, step_size: float, x_end: float
) -> np.ndarray:
"""Calculate numeric solution at each step to an ODE using Euler's Method

For reference to Euler's method refer to https://en.wikipedia.org/wiki/Euler_method.

Args:
ode_func (Callable):  The ordinary differential equation
as a function of x and y.
y0 (float): The initial value for y.
x0 (float): The initial value for x.
step_size (float): The increment value for x.
x_end (float): The final value of x to be calculated.

Returns:
np.ndarray: Solution of y for every step in x.

>>> # the exact solution is math.exp(x)
>>> def f(x, y):
...     return y
>>> y0 = 1
>>> y = explicit_euler(f, y0, 0.0, 0.01, 5)
>>> y[-1]
144.77277243257308
"""
n = int(np.ceil((x_end - x0) / step_size))
y = np.zeros((n + 1,))
y[0] = y0
x = x0

for k in range(n):
y[k + 1] = y[k] + step_size * ode_func(x, y[k])
x += step_size

return y

if __name__ == "__main__":
import doctest

doctest.testmod()
```