Explore BrainMass

Explore BrainMass

    solving differential equations

    Not what you're looking for? Search our solutions OR ask your own Custom question.

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

    Please see the attached file for full description.

    1. Find both the first and second order differentials (y' and y") for the following functions:

    2. Use integrating factor to convert the following equation into "exact ODE" form and solve for y.
    2xy' = (y -x) (y + x)/ y

    3. Solve the differential equation, y is a function of x
    y'' - 6y' + 9y = x^2x

    4. Solve the differential equation, y is a function of x
    2y'' - 2y' + 5y = cos(x), y(0) = 1, y'(0) = 2

    5. Solve the differential equation, y is a function of x
    y'= 2x + 2xy, y(1)= 2

    © BrainMass Inc. brainmass.com March 4, 2021, 11:33 pm ad1c9bdddf
    https://brainmass.com/math/calculus-and-analysis/solving-differential-equations-433751

    Attachments

    Solution Preview

    ET 7430

    1. Find both the first and second order differentials (y' and y") for the following functions:
    
    a.
    Using the product rule and chain rule:

    Then the second derivative is:

    b.

    Then the second derivative is:

    c.
    Apply the chain rule:

    Apply the product rule and chain rule:

    2. Use integrating factor to convert the following equation into "exact ODE" form and solve for y.

    Rearrange the equation:

    
    Then

    And
    is a function of x alone, then
    is an integrating factor.
    So multiplying 1/x2 to the equation (1):

    (2)
    Whose ...

    Solution Summary

    It provides detailed explanations of different methods of solving differential equations, such as converting to exact ODE, undetermined coefficient method, and separation of variables.

    $2.49

    ADVERTISEMENT