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

Lösung

y e^{x} \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

y e^{x} \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

x \frac{d y}{d x} = y^{2} - 9

x^{3} y^{^{'}} = 1 + y

(x^{2} + 9) \frac{d y}{d x} = x y

y^{^{'}} = x y^{2} sin (x^{2}), y (0) = 1

y^{^{'}} = y^{2} + 1