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    Ordinary differential equations

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    I would like someone to introduce me to ODE and answer questions as they arise.

    © BrainMass Inc. brainmass.com March 6, 2023, 1:12 pm ad1c9bdddf

    Solution Preview

    ODE is the part of calculus where both integration as well as differentiation are used..
    simple equation:
    dy/dx = f(x) : degree 1, order 1.
    ORDER of eqn. : order of highest derivative
    DEGREE of eqn.: index or power or raised to the highest order derivative
    e.g. (dy/dx)^3 + (d^2y/dx^2)^2 : order 2, degree 2 (not 3)
    e.g. eqn: dy/dx = sin(x)
    solution=> dy = sin(x). dx
    => y = integration[sin(x)]dx = -cos(x) + const.

    One step ahead:
    dy/dx = f(x,y) : order 1, degree 1
    e.g dy/dx = sin(x)/{sec(y).tan(y)}
    => sec(y).tan(y) dy = sin(x) dx
    => int[sec(y).tan(y)] dy = int[sin(x)] dx
    => sec(y) = ...

    Solution Summary

    This provides a brief introduction to ordinary differential equations. The ordinary differential equation integration is examined.