Explore BrainMass

Explore BrainMass

    First Order Differential Equation.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Consider the ODE y' = y2/x subject to the boundary condition y(1)=1. Find an implicit solution of the form H(x,y) = constant, then find an explicit solution of the form y=y(x). What is the largest x-interval on which the solution is defined?

    *(Please see attachment for proper citation of symbols and numbers)

    © BrainMass Inc. brainmass.com March 4, 2021, 6:04 pm ad1c9bdddf
    https://brainmass.com/math/calculus-and-analysis/ode-boundary-condition-implicit-explicit-solutions-26895

    Attachments

    Solution Preview

    Hi There,

    Here is the solution.
    The first part is finding an integration factor for a non-exact equation.
    The full process is described in:
    http://sosmath.com/diffeq/first/exact/exact.html
    http://sosmath.com/diffeq/first/intfactor/intfactor.html

    -----------

    The equation

    Can be rewritten as:

    This is a non exact equation ...

    Solution Summary

    A step by step process, the solution illustrates two methods to solve the equation. The solution is five pages long of full derivations.

    $2.19

    ADVERTISEMENT