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

Lösung

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

y = - \frac{ln ( - x ^{2} + 4 x - c _{1} )}{2}

Schritte zur Lösung

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

Solve separable ODE:

y = - \frac{ln ( - x ^{2} + 4 x - c _{1} )}{2}

y = - \frac{ln ( - x ^{2} + 4 x - c _{1} )}{2}

\frac{d x}{d y} = e^{x}

3 e^{- 2 y} x^{2} + 8 x e^{- 2 y} = \frac{d y}{d x}

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

x y^{^{'}} = y^{2} - 1

\frac{x ^{3} + 1}{x ^{2}} \frac{d y}{d x} = \frac{1}{y}