Find the function y(x) satisfying dy/dx=8x-3 and y(2)=0y(x)=?

Question

Find the function y(x) satisfying dy/dx=8x-3 and y(2)=0y(x)=?

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Audrey 1 week 2021-09-15T02:42:02+00:00 1 Answer 0

Answers ( )

  1. Charlotte
    0
    2021-09-15T02:44:00+00:00

    Answer:

    y(x)=4x^2 -3x -10

    Step-by-step explanation:

    First take the integral of dy/dx to find a general formula for y(x):

    \frac{dy}{dx} =8x-3\\y(x) = \int{(8x-3)} \, dx =4x^2 -3x +c

    Then, evaluate the expression found above at y(2)=0 in order to find the value for the constant ‘c’:

    y(x) = 4x^2 -3x +c\\y(2) = 0\\0= 4*(2)^2 -(3*2) +c\\c=6-16 = -10

    The expression for y(x) that satisfies both conditions is:

    y(x)=4x^2 -3x -10

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