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Math Help - simple integrating factors problem.. cant see what im doing wrong

  1. #1
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    simple integrating factors problem.. cant see what im doing wrong

    y'+2y=2-e^(-4t)

    this is about as simple as they come.. my integrating factor is e^2t.. after multiplying through i can seperate into product rule, etc. but, when i integrate the right side there's that 2 there.. thats always going to yield a t term when integrated.. however the answer doesnt have that.. its
    y(t) = C e^(-2 t)+e^(-4 t)/2+1

    what happens to the t? or what am i doing wrong?

    also, 1 more thing ( if youd be so kind), i got this example from http://tutorial.math.lamar.edu/Class...ersMethod.aspx

    its the first example.. eulers wasnt too well went over in my class, and (apart from not understanding where the solution to initial problem comes from, which i really should know), im not positive how they go about getting the values for .2,.3, etc. i can follow his work to get .9 as the answer to .1, but he skips over hot to get the rest.. i dont see how the first can be a nice clean .9, but the rest are super long decimals. where does he go next?

    really appreciate some quick help with this as i got a final coming up in a little more than 24 hours -_-
    Last edited by twostep08; April 30th 2011 at 11:29 PM.
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  2. #2
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    Quote Originally Posted by twostep08 View Post
    y'+2y=2-e^(-4t)

    this is about as simple as they come.. my integrating factor is e^2t.. after multiplying through i can seperate into product rule, etc. but, when i integrate the right side there's that 2 there.. thats always going to yield a t term when integrated.. however the answer doesnt have that.. its
    y(t) = C e^(-2 t)+e^(-4 t)/2+1

    what happens to the t? or what am i doing wrong?

    also, 1 more thing ( if youd be so kind), i got this example from Pauls Online Notes : Differential Equations - Euler's Method

    its the first example.. eulers wasnt too well went over in my class, and (apart from not understanding where the solution to initial problem comes from, which i really should know), im not positive how they go about getting the values for .2,.3, etc. i can follow his work to get .9 as the answer to .1, but he skips over hot to get the rest.. i dont see how the first can be a nice clean .9, but the rest are super long decimals. where does he go next?

    really appreciate some quick help with this as i got a final coming up in a little more than 24 hours -_-
    The answer is e^{-2t} \int e^{2t} \left( 2 - e^{-4t} \right) \, dt, which integrates just fine to give the correct answer. Without seeing all your working I cannot say what error(s) you have made.
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  3. #3
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    just found my mistake.. i forgot to multiple the right side too :/

    anyways, thats the first part of this question (the above is the initial condition when y(0)=1:
    Use Euler’s Method with a step size of h = 0.1 to find approximate values of the solution at t = 0.1, 0.2, 0.3, 0.4, and 0.5. Compare them to the exact values of the solution as these points.

    i see what they did to approximate t=.1, but i cant understand how to do the others..
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