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Help With Solving This Differential Equation

  1. Feb 27, 2012 #1
    1. The problem statement, all variables and given/known data

    1. The slope of a function at any point (x,y) is 〖2e〗^x/(e^x+2) . The point (0,2ln3) is on the graph of f.

    (A) Write an equation of the tangent line to the graph of f at x=0.
    (B) Use the tangent line in part A to approximate f(0.3) to the nearest thousandth.
    (C) Solve the differential equation dy/(dx )=(2e^x)/(e^x+2) with the initial condition f(0)=2ln3.
    (D) Use the solution in part C to find f(0.3) to the nearest thousandth.

    2. Relevant equations

    3. The attempt at a solution


    dy/(dx )=(2e^x)/(e^x+2)

    At x=0, dy/dx=(2e^0)/(e^0+2)=2/3

    Equation of tangent line at x=0: y-2ln3=2/3 (x-0)

    y-2ln3=2/3 x or y=2/3 x+2ln3


    f(0.3)≈2/3 (0.3)+2ln3≈2.39722≈2.397


    dy/dx=〖2e〗^x/(e^x+2) → dy=(2e^x)/(e^x+2) → ∫dy= ∫〖(2e^x)/(e^x+2) dx〗

    Let u=e^x+2, du=e^x dx

    Here is where I run into problems. Can anybody help me with the rest? Any help would be greatly appreciated.
  2. jcsd
  3. Feb 27, 2012 #2
    bump. please, i'm desperate for help.
  4. Feb 27, 2012 #3


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    Staff Emeritus
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    Rewrite your integral in terms of the variable, u .
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