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    Ok, ok.... I totally don't get this....
    Lets deal with the RHS first, they're integrating t^2 with respect to t, should that not be (1/3).t^3 + C???

    And the LHS, where the hell did dx come from?! How did they get the integral on the LHS?!

    I'm hopeless....
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    The dx was probably a mistake. The y (with the dot) implies \frac{dy}{dt}

    So it really should have been dy.

    And yes, they did intergrate the RHS, but they simplified it. Try it yourself, and multiply by 6. You will get the correct anwser.
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    Hahaha, I was trying to find some magical way of integrating with respect to x......
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    Remember y(dot) = dy/dt

    so the question is dy/dt = t^2/(y + e^y)

    Separating variables (ie putting all of one variable on one side of the equation and treating the differential symbol as a fraction) and putting in the integral signs we get

    Int (y + e^y ) dy = Int (t^2) dt

    So (1/2)y^2 + e^y = (1/3)t^3 + c

    Multiplying through by 3 gives

    (3/2)y^2 + 3e^y = t^3 +c

    Multiplying through by 2 gives:

    3y^2 + 6e^y = 2t^3 + c

    (I'm assuming here you understand the method of integration by separating variables, so I've just explain what you do in practice, rather than why we do it and why it works )
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    (Original post by Roger Kirk)
    Remember y(dot) = dy/dt

    so the question is dy/dt = t^2/(y + e^y)

    Separating variables (ie putting all of one variable on one side of the equation and treating the differential symbol as a fraction) and putting in the integral signs we get

    Int (y + e^y ) dy = Int (t^2) dt

    So (1/2)y^2 + e^y = (1/3)t^3 + c

    Multiplying through by 3 gives

    (3/2)y^2 + 3e^y = t^3 +c

    Multiplying through by 2 gives:

    3y^2 + 6e^y = 2t^3 + c

    (I'm assuming here you understand the method of integration by separating variables, so I've just explain what you do in practice, rather than why we do it and why it works )
    Yeah I do, I just haven't slept and thus I was trying to integrate with respect to x, blindly following the question..... Thanks tho!!
 
 
 
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