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Math Help - differencial equation

  1. #1
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    differencial equation

    Heres the question, i been working on it for a while but i cant seem to get it rite..please help!

    1. A hole is drilled in a sheet-metal component, and then a shaft is inserted through the hole. The shaft clearance is equal to the difference between the radius of the hole and the radius of the shaft. Let the random variable X denote the clearance, in millimeters. The probability density function of X is

    f(x) = 1.5(1-x^4) 0<x<1

    0 otherwise

    Components with clearances larger than 0.8 mm must be scrapped. What proportion of components are scrapped?

    Find the mean clearance.
    2. Find the solution of the differential equation xy' + y = y^2that satisfies the initial condition of y(1)= -1


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  2. #2
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    Quote Originally Posted by sikhest View Post
    .
    2. Find the solution of the differential equation xy' + y = y^2that satisfies the initial condition of y(1)= -1
    Hint: Write as (y-y^2)+xy'=0.
    Let M(x,y)=y-y^2 \mbox{ and }N(x,y)=x
    Note that,
    \frac{\frac{\partial M}{\partial y} - \frac{\partial N}{\partial x}}{M(x,y)}
    Is a function of only y.

    So you can multiply through an integrating factor and bring it to exact form.
    Klicken Heir.
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  3. #3
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    Quote Originally Posted by sikhest View Post
    2. Find the solution of the differential equation xy' + y = y^2that satisfies the initial condition of y(1)= -1
    Rewrite this equation as \frac{{y'}}<br />
{{y^2 }} + \frac{{x^{ - 1} }}<br />
{y} = x^{ - 1}

    Now set u=\frac1{y}

    After this, you'll have an equation of the form y\,'+P(x)y=Q(x)
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