calculus

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How do you solve the initial value problem?

(dy/dx)-2y+4=0, y(1)=4

  • calculus -

    I am going to use t instead of x. I can do initial condition better that way
    let y = a e^kt + b
    dy/dt = a k e^kt

    a k e^kt -2 a e^kt -2b + 4 = 0

    so b = 2
    a k = 2 a
    k = 2

    y = a e^2t + 2
    when t = 1, y = 4
    4 = a e^2 +2
    a e^2 = 2
    a = 2/e^2
    so
    y = (2/e^2) e^2t + 2
    y = 2 e^(2t-2) + 2

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