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

Lösung

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

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

Schritte zur Lösung

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

Solve Bernoulli ODE:

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

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

d er i v a t i v e f (x) = 2 e^{2}

\frac{d x}{d t} = sin (π x)

\frac{d}{d x} (ln (x^{2} + y^{2} + 1))

x \to \infty + lim (\frac{( 5 x ^{3} + 7 x ^{2} - 8 x + 9 )}{11 x ^{2} + 7 x - 6})

\int sin^{4} (7 x) d x