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Math Help - Differential equations, separating variables!

  1. #1
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    Differential equations, separating variables!

    if we have dy/dx=e^(2x-1) how do we find the general solution??? help much appreciated!! thankyou!!
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  2. #2
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    It's a matter of simple integration. You know that [e^x]'=e^x, so

    [\frac{1}{2}e^{2x-1}]'=e^{2x-1}

    A general solution is thus

    y(x)=\frac{1}{2}e^{2x-1}+C (with C\in \mathbb R
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  3. #3
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    Quote Originally Posted by Nyrox View Post
    It's a matter of simple integration. You know that [e^x]'=e^x, so

    [\frac{1}{2}e^{2x-1}]'=e^{2x-1}

    A general solution is thus

    y(x)=\frac{1}{2}e^{2x-1}+C (with C\in \mathbb R
    Yes thank you!! that's right, can you just help me with 2 other problems?

    firstly, if i have the function cosx-sinx=0 how do i solve it? im stumped :/

    and secondly how to i find the volum of space if the function x^(1/2)*e^x revolved around the x axis 360 degrees with the limits 1 and 2?

    Thanks a million!!!!!
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  4. #4
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    Quote Originally Posted by Yehia View Post
    firstly, if i have the function cosx-sinx=0 how do i solve it? im stumped :/
    \cos x - \sin x = 0

    \cos x = \sin x

    \frac{\sin x}{\cos x} = 1

    \tan x = 1
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  5. #5
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    These have nothing to do with your original question... But anyway, for the first one, plot the graphs of both sine and consine, and you'll get your answer. As for the second, you must've seen the connection between the integral and a solid obtain by revolution. Calling V the volume of the solid obtained by revolving a curve f(x) around the x axis between points a and b:

    V=\int_a^b\pi (f(x))^2 \, dx
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  6. #6
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    Quote Originally Posted by Yehia View Post
    Yes thank you!! that's right, can you just help me with 2 other problems?

    firstly, if i have the function cosx-sinx=0 how do i solve it? im stumped :/

    and secondly how to i find the volum of space if the function x^(1/2)*e^x revolved around the x axis 360 degrees with the limits 1 and 2?

    Thanks a million!!!!!
    Already answered on the first one; on the volume question, I would use integration by parts - but it looks nasty. Is this equation written correctly?
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  7. #7
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    Quote Originally Posted by ANDS! View Post
    Already answered on the first one; on the volume question, I would use integration by parts - but it looks nasty. Is this equation written correctly?
    yes it is but im unfamiliar with writing it on these threads :S ill try:

    f(x)=x^{1/2}e^x

    made it!
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  8. #8
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    Quote Originally Posted by Yehia View Post
    yes it is but im unfamiliar with writing it on these threads :S ill try:

    f(x)=x^{1/2}e^x

    made it!
    I see no method to solve that problem unfortunately. Integration by parts will get you no where, and there is no method (that I know of), that will let you itegrate that sucker easily. What level math is this from? I can not imagine, if you are doing volumes of solids of revolution - which is Integral Calculus (or Calc 2), that they would ask you to do this problem.
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