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Learning Differential equations, week 2 level material

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  1. Oct 1, 2015 #1
    1. The problem statement, all variables and given/known data

    Find the general solution to the equation.

    2. Relevant equations
    (dy/dx) - y - e^3x=0

    3. The attempt at a solution

    I rewrote this as dy/dx - y = e^3x

    This is a linear first order ODE, in the form dy/dx + P(x)y = f(x)

    P(x) = 1; f(x) = e^3x

    The integrating factor = e^(integral)P(x) dx = e^(integral) 1* dx = e^x

    Set the LHS equal to the integrating factor, e^x * y, and multiply the RHS by the integrating factor e^x)

    d/dx (ye^x) = e^x e^3x

    (integral) d/dx (ye^x) =(integral) e^(3x^2) dx

    On the LHS, the integral and d/dx cancel out, but I am getting a ridiculously complicated integral that I just know isn't right on the RHS, and I am not sure where I went astray.

    Thank you for your time,

    SY
     
  2. jcsd
  3. Oct 1, 2015 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    [itex]e^xe^{3x}= e^{4x}[/itex], NOT [itex]e^{3x^2}[/itex].
     
  4. Oct 1, 2015 #3

    Mark44

    Staff: Mentor

    Please use parentheses where needed. e^3x would normally be interpreted as ##e^3 \cdot x##. In your first equation above, you have parentheses around dy/dx, where they aren't needed, but don't have them around the exponent 3x, where they are needed.

    BTW, I changed the thread title to say "... week 2 level material". I think that's what you intended.
     
  5. Oct 1, 2015 #4
    will do, thank you
     
  6. Oct 1, 2015 #5
    Thank you, that is not the first silly mistake I will make, and will not be the last...
     
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