What is the solution for (dy)/(dx)= 1/(xsqrt(16x^2-1)) ?

The solution for (dy)/(dx)= 1/(xsqrt(16x^2-1)) is y=arctan(sqrt(16x^2-1))+c_{1}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(dy)/(dx)= 1/(xsqrt(16x^2-1))

\frac{d y}{d x} = \frac{1}{x 16 x ^{2} - 1}

y = arctan (16 x^{2} - 1) + c_{1}

Solution steps

\frac{d y}{d x} = \frac{1}{x 16 x ^{2} - 1}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = \frac{1}{x 16 x ^{2} - 1}

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

then

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

y = \int \frac{1}{x 16 x ^{2} - 1} d x

\int \frac{1}{x 16 x ^{2} - 1} d x = arctan (16 x^{2} - 1) + c_{1}

y = arctan (16 x^{2} - 1) + c_{1}

What is the solution for (dy)/(dx)= 1/(xsqrt(16x^2-1)) ?
The solution for (dy)/(dx)= 1/(xsqrt(16x^2-1)) is y=arctan(sqrt(16x^2-1))+c_{1}