(dy)/(dx)= 4/(x^2-1)

解

\frac{d y}{d x} = \frac{4}{x ^{2} - 1}

y = - 4 (\frac{1}{2} ln (x + 1) - \frac{1}{2} ln (x - 1)) + c_{1}

解答ステップ

\frac{d y}{d x} = \frac{4}{x ^{2} - 1}

代用

\frac{d y}{d x}

と

y^{'} (x)

y^{^{'}} (x) = \frac{4}{x ^{2} - 1}

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

であれば

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

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

\int \frac{4}{x ^{2} - 1} d x = - 4 (\frac{1}{2} ln (x + 1) - \frac{1}{2} ln (x - 1)) + c_{1}

y = - 4 (\frac{1}{2} ln (x + 1) - \frac{1}{2} ln (x - 1)) + c_{1}