What is expand (3ydx+6dx-xdy=0) 1/(xdx) ?

The solution to expand (3ydx+6dx-xdy=0) 1/(xdx) is (3y)/x+6/x-(dy)/(dx)=0

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expand (3ydx+6dx-xdy=0) 1/(xdx)

expand

(3 y d x + 6 d x - x d y = 0) \frac{1}{x d x}

\frac{3 y}{x} + \frac{6}{x} - \frac{d y}{d x} = 0

Solution steps

(3 y d x + 6 d x - x d y = 0) \frac{1}{x d x}

= \frac{1}{x d x} (3 y d x + 6 d x - 0 = x d y)

Distribute parentheses

= \frac{1}{x d x} \cdot 3 y d x + \frac{1}{x d x} \cdot 6 d x + \frac{1}{x d x} (- x d y = 0)

Apply minus-plus rules

+ (- a) = - a

3 \cdot \frac{1}{x d x} y d x + 6 \cdot \frac{1}{x d x} d x - \frac{1}{x d x} x d y = 0

Expand

3 \cdot \frac{1}{x d x} y d x + 6 \cdot \frac{1}{x d x} d x - \frac{1}{x d x} x d y : \frac{3 y}{x} + \frac{6}{x} - \frac{d y}{d x}

\frac{3 y}{x} + \frac{6}{x} - \frac{d y}{d x} = 0

2 (x^{2} + 4 x + 8)^{2}

(2 x^{2} + 3 x) e^{x}

\frac{d}{d t} ((x) (4 (x^{2} + 1)))

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

x^{2} + 1^{2}

What is expand (3ydx+6dx-xdy=0) 1/(xdx) ?
The solution to expand (3ydx+6dx-xdy=0) 1/(xdx) is (3y)/x+6/x-(dy)/(dx)=0