What is expand y(y^2+1)dx+x(y^2-1)ln(x)dy ?

The solution to expand y(y^2+1)dx+x(y^2-1)ln(x)dy is y^3dx+ydx+y^2xln(x)dy-xln(x)dy

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expand y(y^2+1)dx+x(y^2-1)ln(x)dy

expand

y (y^{2} + 1) d x + x (y^{2} - 1) ln (x) d y

y^{3} d x + y d x + y^{2} x ln (x) d y - x ln (x) d y

Solution steps

y (y^{2} + 1) d x + x (y^{2} - 1) ln (x) d y

= y (y^{2} + 1) d x + x ln (x) (y^{2} - 1) d y

Expand

y d x (y^{2} + 1) : y^{3} d x + y d x

= y^{3} d x + y d x + x (y^{2} - 1) ln (x) d y

Expand

x ln (x) d y (y^{2} - 1) : y^{2} x ln (x) d y - x ln (x) d y

= y^{3} d x + y d x + y^{2} x ln (x) d y - x ln (x) d y

(x - 1)^{3} (\frac{1}{x} + x)^{6}

\frac{3}{( 6 + x ) ^{3}}

(x - \frac{1}{x ^{2}}) \cdot (x + \frac{1}{x ^{2}})

cos (2 x^{3} - 9 x) (6 x^{2} - 9)

- 2 (2 + 3) 2 - 3

What is expand y(y^2+1)dx+x(y^2-1)ln(x)dy ?
The solution to expand y(y^2+1)dx+x(y^2-1)ln(x)dy is y^3dx+ydx+y^2xln(x)dy-xln(x)dy