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Math Help - [SOLVED] Calculus differential equation

  1. #1
    jet2479
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    [SOLVED] Calculus differential equation

    Solve the following differential equations

    a) dy/dx = 24x(3x^2+9)^2

    b) dy/dx = 2sin(3x+infinity) infinity is a constant

    I have done question a and come up with 216x^5+1296x^3+1944x

    I don't know if this is right.

    Please give me some tips on how to do these.

    Cheers
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by jet2479 View Post
    Solve the following differential equations

    a) dy/dx = 24x(3x^2+9)^2
    these are among the easiest types of differential equations you will get. just integrate both sides.


    \frac {dy}{dx} = 24x \left( 3x^2 + 9 \right)^2

    \Rightarrow y = 24 \int \left( 3x^2 + 9 \right)^2~dx

    We proceed by substitution.

    Let u = 3x^2 + 9

    \Rightarrow du = 6x ~dx

    \Rightarrow \frac {1}{6}~du = dx

    So we have:

    y = \frac {24}{6} \int u^2 ~du

    \Rightarrow y = \frac {4}{3} u^3 + C

    \Rightarrow y = \frac {4}{3} \left( 3x^2 + 9 \right)^3 + C


    b) dy/dx = 2sin(3x+infinity) infinity is a constant
    "infinity is a constant," now there's a thought!

    same story here, integrate both sides. you try this one
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