What is the solution for (dy)/(dx)=(9x^2-6)/(x^2) ?

The solution for (dy)/(dx)=(9x^2-6)/(x^2) is y=9x+6/x+c_{1}

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(dy)/(dx)=(9x^2-6)/(x^2)

\frac{d y}{d x} = \frac{9 x ^{2} - 6}{x ^{2}}

y = 9 x + \frac{6}{x} + c_{1}

Solution steps

\frac{d y}{d x} = \frac{9 x ^{2} - 6}{x ^{2}}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = \frac{9 x ^{2} - 6}{x ^{2}}

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

then

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

y = \int \frac{9 x ^{2} - 6}{x ^{2}} d x

\int \frac{9 x ^{2} - 6}{x ^{2}} d x = 9 x + \frac{6}{x} + c_{1}

y = 9 x + \frac{6}{x} + c_{1}

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What is the solution for (dy)/(dx)=(9x^2-6)/(x^2) ?
The solution for (dy)/(dx)=(9x^2-6)/(x^2) is y=9x+6/x+c_{1}