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

Lösung

\frac{1}{x} \frac{d y}{d x} = e^{x - y} + e^{- y}

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

Schritte zur Lösung

\frac{1}{x} \frac{d y}{d x} = e^{x - y} + e^{- y}

Solve separable ODE:

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

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

y^{^{'}} = - \frac{x - 3}{y - 8}, y (3) = 10

+ x ye d y + 4 x d x = 0

y^{^{'}} = - x^{2} y^{2}

\frac{d y}{d x} = 2 x y^{3}

9 x t^{2} = \frac{d x}{d t}