Let y=f(x) be the particular solution to the differential equation dy/dx=2x−1/y^2 with the initial condition y(0)=3. Which of the following

Question

Let y=f(x) be the particular solution to the differential equation dy/dx=2x−1/y^2 with the initial condition y(0)=3. Which of the following is an expression for f(x)?
A. √(x^2−x+9)

B. −3/3x^2−3x−1

C. (3x^2−3x)^1/3+3

D. (3x^2−3x+27)^1/3

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Linh Đan 3 years 2021-08-27T12:06:13+00:00 2 Answers 71 views 0

Answers ( )

  1. hongcuc2
    0
    2021-08-27T12:07:19+00:00
    Reply

    Answer:

    D. (3x^2-3x+27)^1/3

    Step-by-step explanation:

    dy/dx=2x−1/y^2

    Cross multiply to get Y’s and X’s on different sides.

    (y^2)dy = (2x-1)dx

    Take the integral of each side

    ∫(y^2)dy = ∫(2x-1)dx

    y^3/3 = 2x^2/2 – x + C

    Multiply both sides by 3

    y^3 = 3x^2 – 3x + C

    Plug in (0,3) and solve for C

    27 = 0 – 0 + C

    C = 27

    Plug in C to the equation

    y^3 = 3x^2-3x+27

    Cube root both sides to get just y

    y = √(3x^2-3x+27)

    y = (3x^2-3x+27)^1/3

    D.

  2. ThanhThu
    0
    2021-08-27T12:07:25+00:00
    Reply

    Answer:

    its D, i did it for an exam

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