What is the solution for (dy)/(dx)= 1/(2x(7-x)) ?

The solution for (dy)/(dx)= 1/(2x(7-x)) is y= 1/2 (1/7 ln(x)-1/7 ln(x-7))+c_{1}

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(dy)/(dx)= 1/(2x(7-x))

\frac{d y}{d x} = \frac{1}{2 x ( 7 - x )}

y = \frac{1}{2} (\frac{1}{7} ln (x) - \frac{1}{7} ln (x - 7)) + c_{1}

Solution steps

\frac{d y}{d x} = \frac{1}{2 x ( 7 - x )}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = \frac{1}{2 x ( 7 - x )}

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

y = \int \frac{1}{2 x ( 7 - x )} d x

\int \frac{1}{2 x ( 7 - x )} d x = \frac{1}{2} (\frac{1}{7} ln (x) - \frac{1}{7} ln (x - 7)) + c_{1}

y = \frac{1}{2} (\frac{1}{7} ln (x) - \frac{1}{7} ln (x - 7)) + c_{1}

y^{^{'}} - 3 x^{2} y = 12 x^{2}

(5 x^{2} - 8 x) e^{x}

\int \frac{1}{1 - 4 x ^{2}} d x

f (x) = - 5 - 3 x^{2}, - 53, at x = 4

(- 3.2) (7.6)

What is the solution for (dy)/(dx)= 1/(2x(7-x)) ?
The solution for (dy)/(dx)= 1/(2x(7-x)) is y= 1/2 (1/7 ln(x)-1/7 ln(x-7))+c_{1}