y^'=(e^x-e^{-x})/(3+4y)

解

y^{^{'}} = \frac{e ^{x} - e ^{- x}}{3 + 4 y}

y = \frac{- 3 + 9 - 8 ( - c _{1} - 2 cosh ( x ) )}{4}, y = \frac{- 3 - 9 - 8 ( - c _{1} - 2 cosh ( x ) )}{4}

解答ステップ

y^{'} (x) = \frac{e ^{x} - e ^{- x}}{3 + 4 y}

分離可能 ODE を解く:

y = \frac{- 3 + 9 - 8 ( - c _{1} - 2 cosh ( x ) )}{4}, y = \frac{- 3 - 9 - 8 ( - c _{1} - 2 cosh ( x ) )}{4}

y = \frac{- 3 + 9 - 8 ( - c _{1} - 2 cosh ( x ) )}{4}, y = \frac{- 3 - 9 - 8 ( - c _{1} - 2 cosh ( x ) )}{4}