I am solving the equation \(\displaystyle \, \left(2x^2y\, +\, y^3\right) dx\, +\, \left(xy^2\, -\, 2x^3\right) dy\, =\, 0\,\) by using the substitutions \(\displaystyle \,x\,=\,uy\,\) and \(\displaystyle \, dx\, =\, ydu\, +\, udy.\,\) Doing this gives me the implicit solution:
. . .\(\displaystyle \ln\Bigg|\, xy\, \Bigg|\, +\, \left(\dfrac{x}{y}\right)^2\, =\, c\)
My answer key gives me the same solution without the absolute value bars, but I can't figure out how I can drop them.
Thanks for reading.
. . .\(\displaystyle \ln\Bigg|\, xy\, \Bigg|\, +\, \left(\dfrac{x}{y}\right)^2\, =\, c\)
My answer key gives me the same solution without the absolute value bars, but I can't figure out how I can drop them.
Thanks for reading.
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