(dy)/(dx)y=cos^{-1}(1/x)

解

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

y = 2 x arccos (\frac{1}{x}) - ln (\frac{x ^{2} - 1}{x} + 1) + ln (\frac{x ^{2} - 1}{x} - 1) + c_{1}, y = - 2 x arccos (\frac{1}{x}) - ln (\frac{x ^{2} - 1}{x} + 1) + ln (\frac{x ^{2} - 1}{x} - 1) + c_{1}

解答ステップ

\frac{d y}{d x} y = arccos (\frac{1}{x})

分離可能 ODE を解く:

y = 2 x arccos (\frac{1}{x}) - ln (\frac{x ^{2} - 1}{x} + 1) + ln (\frac{x ^{2} - 1}{x} - 1) + c_{1}, y = - 2 x arccos (\frac{1}{x}) - ln (\frac{x ^{2} - 1}{x} + 1) + ln (\frac{x ^{2} - 1}{x} - 1) + c_{1}

y = 2 x arccos (\frac{1}{x}) - ln (\frac{x ^{2} - 1}{x} + 1) + ln (\frac{x ^{2} - 1}{x} - 1) + c_{1}, y = - 2 x arccos (\frac{1}{x}) - ln (\frac{x ^{2} - 1}{x} + 1) + ln (\frac{x ^{2} - 1}{x} - 1) + c_{1}