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John H
Lv 5
John H asked in Science & MathematicsMathematics · 9 years ago

Differential Equation Help Please!?

Solve the separable differential equation for

du/dt=e^(6u+2t)

Use the following initial condition:u(0)=-13 . u=?

Update:

Please Help

2 Answers

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  • ted s
    Lv 7
    9 years ago
    Favourite answer

    you certainly can do the work.....e^( - 6 u ) du = e^( 2 t ) dt , integrate , side condition to find C

  • Rapidfire
    Lv 7
    9 years ago

    Find the general solution by separating the variables then integrating:

    du / dt = ℮^(6u + 2t)

    du / dt = ℮^(6u)℮^(2t)

    du / ℮^(6u) = ℮^(2t) dt

    ℮^(-6u) du = ℮^(2t) dt

    ∫ ℮^(-6u) du = ∫ ℮^(2t) dt

    -℮^(-6u) / 6 = ℮^(2t) / 2 + C

    ℮^(-6u) = C - 3℮^(2t)

    -6u = ln[C - 3℮^(2t)]

    u = -ln[C - 3℮^(2t)] / 6

    Find the particular solution by solving for the constant:

    When t = 0, u = -13

    -ln(C - 3) / 6 = -13

    ln(C - 3) = 78

    C - 3 = ℮⁷⁸

    C = 3 + ℮⁷⁸

    u = -ln[3 + ℮⁷⁸ - 3℮^(2t)] / 6

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