What is the solution for (dy)/(dx)=(x/(sqrt(1-6x^2))) ?

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

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(dy)/(dx)=(x/(sqrt(1-6x^2)))

\frac{d y}{d x} = (\frac{x}{1 - 6 x ^{2}})

y = - \frac{1}{6} 1 - 6 x^{2} + c_{1}

Solution steps

\frac{d y}{d x} = (\frac{x}{1 - 6 x ^{2}})

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = (\frac{x}{1 - 6 x ^{2}})

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

then

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

y = \int \frac{x}{1 - 6 x ^{2}} d x

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

y = - \frac{1}{6} 1 - 6 x^{2} + c_{1}

\int (10 x^{3} + \frac{7}{x ^{2}} - x) d x

\int 2 x cos (x) - cos^{2} (x) d x

\int_{0}^{2} \frac{2}{16 - x ^{2}} d x

\int cot^{3} (4 x) d x

f (x) = \frac{4 x}{x + 2}, at x = 6

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