Explore BrainMass

Explore BrainMass

    Differential Equation : Basis

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

    Verify that the given functions form a basis for the space of solutions of the given differential equation:
    x^2 y'' - 2xy' + 2y = 0, f_1(x) = x, f_2(x) = x^2, x > 0

    © BrainMass Inc. brainmass.com February 24, 2021, 2:21 pm ad1c9bdddf
    https://brainmass.com/math/calculus-and-analysis/differential-equation-basis-16074

    Solution Preview

    Proof. First, we will verify that f_1(x)=x, f_2(x)=x^2 satisfy the differential equation x^2y''-2xy'+2y=0

    (1) y=f_1(x)=x
    y'=1, y''=0
    ...

    Solution Summary

    It is verified that functions form a basis for the space of solutions of a differential equation.

    $2.19

    ADVERTISEMENT