can't separate anything from this DE :

$\displaystyle (xy'-y)^2=y'^2-2yy'/x+1$

tried to group something but it didn't help

$\displaystyle x^2y'(xy'-2y)+xy^2=y'(xy'-2y)+x$

and the second problem is this below

Results 1 to 5 of 5

- Apr 4th 2010, 12:21 AM #1

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- Apr 4th 2010, 04:58 AM #2
For problem 1) Multiply by $\displaystyle x^2$ so

$\displaystyle

x^2 \left(x y' - y\right)^2 = x^2 y'^2 - 2 x y' y + x^2

$

so

$\displaystyle

x^2 \left(x y' - y\right)^2 = \left(x y' - y\right)^2 + x^2 - y^2

$

or $\displaystyle x y' - y = \pm \frac{\sqrt{x^2-y^2}}{\sqrt{x^2-1}} $

Then try $\displaystyle y = x u$

Problem 2)

From your answer

$\displaystyle

z'' = \frac{z'}{1+c_1 z'}

$

so

$\displaystyle

\left(1+c_1z'\right)z'' = z'

$

Integrate left and right sides once. See how that goes.

- Apr 4th 2010, 07:03 AM #3

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- Apr 4th 2010, 08:00 AM #4

- Apr 4th 2010, 10:32 AM #5

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