differencial equation

**sikhest** · May 31st 2007, 07:22 AM

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

**ThePerfectHacker** · May 31st 2007, 08:10 AM

Originally Posted by sikhest

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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.

**Krizalid** · May 31st 2007, 08:37 AM

Originally Posted by sikhest

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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