What is expand (y^2+xy^3)dx+(5y^2-xy+y^3sin(y))dy ?

The solution to expand (y^2+xy^3)dx+(5y^2-xy+y^3sin(y))dy is y^2dx+y^3xdx+5y^2dy-yxdy+y^3sin(y)dy

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expand (y^2+xy^3)dx+(5y^2-xy+y^3sin(y))dy

expand

(y^{2} + x y^{3}) d x + (5 y^{2} - x y + y^{3} sin (y)) d y

y^{2} d x + y^{3} x d x + 5 y^{2} d y - y x d y + y^{3} sin (y) d y

Solution steps

(y^{2} + x y^{3}) d x + (5 y^{2} - x y + y^{3} sin (y)) d y

= (y^{2} + y^{3} x) d x + (5 y^{2} - y x + y^{3} sin (y)) d y

Expand

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

= y^{2} d x + y^{3} x d x + (5 y^{2} - x y + y^{3} sin (y)) d y

Expand

d y (5 y^{2} - x y + y^{3} sin (y)) : 5 y^{2} d y - y x d y + y^{3} sin (y) d y

= y^{2} d x + y^{3} x d x + 5 y^{2} d y - y x d y + y^{3} sin (y) d y

(x + sin (x))^{2}

2 (3 + 5)

\frac{- s ^{2} + 6 s - 12}{( s - 2 ) ( s ^{2} - 4 s + 8 )}

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

What is expand (y^2+xy^3)dx+(5y^2-xy+y^3sin(y))dy ?
The solution to expand (y^2+xy^3)dx+(5y^2-xy+y^3sin(y))dy is y^2dx+y^3xdx+5y^2dy-yxdy+y^3sin(y)dy