.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "intro/scipy/auto_examples/plot_solve_ivp_simple.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_intro_scipy_auto_examples_plot_solve_ivp_simple.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_intro_scipy_auto_examples_plot_solve_ivp_simple.py:


=========================
Integrating a simple ODE
=========================

Solve the ODE dy/dt = -2y between t = 0..4, with the initial condition
y(t=0) = 1.

.. GENERATED FROM PYTHON SOURCE LINES 9-33



.. image-sg:: /intro/scipy/auto_examples/images/sphx_glr_plot_solve_ivp_simple_001.png
   :alt: Solution of Initial Value Problem
   :srcset: /intro/scipy/auto_examples/images/sphx_glr_plot_solve_ivp_simple_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import numpy as np
    import scipy as sp
    import matplotlib.pyplot as plt


    def f(t, y):
        return -2 * y


    t_span = (0, 4)  # time interval
    t_eval = np.linspace(*t_span)  # times at which to evaluate `y`
    y0 = [
        1,
    ]  # initial state
    res = sp.integrate.solve_ivp(f, t_span=t_span, y0=y0, t_eval=t_eval)

    plt.figure(figsize=(4, 3))
    plt.plot(res.t, res.y[0])
    plt.xlabel("t")
    plt.ylabel("y")
    plt.title("Solution of Initial Value Problem")
    plt.tight_layout()
    plt.show()


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.073 seconds)


.. _sphx_glr_download_intro_scipy_auto_examples_plot_solve_ivp_simple.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_solve_ivp_simple.ipynb <plot_solve_ivp_simple.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_solve_ivp_simple.py <plot_solve_ivp_simple.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_solve_ivp_simple.zip <plot_solve_ivp_simple.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_