e^xy(dy)/(dx)=e^{-y}+e^{(-2x-y)}

Lösung

e^{x} y \frac{d y}{d x} = e^{- y} + e^{(- 2 x - y)}

y = W (\frac{- \frac{3}{e ^{x}} - \frac{1}{e ^{3 x}} + c _{1}}{3 e}) + 1

Schritte zur Lösung

e^{x} y \frac{d y}{d x} = e^{- y} + e^{(- 2 x - y)}

Solve separable ODE:

y = W (\frac{- \frac{3}{e ^{x}} - \frac{1}{e ^{3 x}} + c _{1}}{3 e}) + 1

y = W (\frac{- \frac{3}{e ^{x}} - \frac{1}{e ^{3 x}} + c _{1}}{3 e}) + 1

y^{^{'}} + y = y (sin (x) + 1)

\frac{d y}{d x} = 2 y tan (x)

(x^{2} + 1) sin (y) y^{^{'}} = - 2 x cos (y)

\frac{d y}{d t} = - 3 y

y^{^{'}} = \frac{x ^{7}}{y ^{8}}