Calculus

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Consider the differential equation,
dy/dx=(x+1)/y^2

with the initial condition y(0)=3.

Write down the particular solution, and hence, calculate the value of y when x=8.7, to 3 dec places.

  • Calculus -

    That can be solved by separation of variables.
    y^2 dy = (x+1) dx

    y^3/3 = x^2/2 + x + C

    If y(0) = 3, then C = 3

    y^3/3 = x^2/2 + x + 3

  • Calculus - note -

    3^3/3 = C
    C = 9

  • Calculus -

    Steve is correct.

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