Solving a Differential Equation with Variables and Steps | Math Homework Help

sedaw
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Homework Statement



y`=(xy-y^2)/x^2

The Attempt at a Solution




y` = y/x -(y/x)^2

{y/x=z , y=zx , y`=z+xz`}

-z^2=x*dz/dx


-z^2dx = xdz


what`s next ?


TNX . :smile:
 
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Next is to move the -z^2 and x factors around so they are with, respectively, dz and dx. Then integrate.
 
To integrate that, you need your z's on one side and your x's on the other. Dividing through by x*z^2 should do the trick.
 
can u write can't understand .

TNX .
 
it`s o k .

TNX
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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