Help With Solving This Differential Equation

  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. bump. please, i'm desperate for help.
  4. SammyS

    SammyS 9,131
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Rewrite your integral in terms of the variable, u .
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