What is (x-yln(y)+yln(x))dx+x(ln(y)-ln(x))dy ?

The solution to (x-yln(y)+yln(x))dx+x(ln(y)-ln(x))dy is (x-yln(y)+yln(x))dx+xln(y/x)dy

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simplify (x-yln(y)+yln(x))dx+x(ln(y)-ln(x))dy

simplify

(x - y ln (y) + y ln (x)) d x + x (ln (y) - ln (x)) d y

(x - y ln (y) + y ln (x)) d x + x ln (\frac{y}{x}) d y

Solution steps

(x - y ln (y) + y ln (x)) d x + x (ln (y) - ln (x)) d y

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (y) - ln (x) = ln (\frac{y}{x})

= (x - y ln (y) + y ln (x)) d x + x ln (\frac{y}{x}) d y

lo g_{5} (\frac{25}{y})

lo g_{8} (x y)

ln (10) - ln (x)

lo g_{4} (\frac{16}{y})

lo g_{10} (2 x + 3) - lo g_{10} (x)

What is (x-yln(y)+yln(x))dx+x(ln(y)-ln(x))dy ?
The solution to (x-yln(y)+yln(x))dx+x(ln(y)-ln(x))dy is (x-yln(y)+yln(x))dx+xln(y/x)dy