y^'+(x+1)y=e^{x^2}y^3

Lösung

y^{^{'}} + (x + 1) y = e^{x^{2}} y^{3}

y = \frac{e ^{- x^{2} - 2 x}}{e ^{- 2 x} + c _{1}}, y = - \frac{e ^{- x^{2} - 2 x}}{e ^{- 2 x} + c _{1}}

Schritte zur Lösung

y^{'} (x) + (x + 1) y = e^{x^{2}} y^{3}

Solve Bernoulli ODE:

y = \frac{e ^{- x^{2} - 2 x}}{e ^{- 2 x} + c _{1}}, y = - \frac{e ^{- x^{2} - 2 x}}{e ^{- 2 x} + c _{1}}

y = \frac{e ^{- x^{2} - 2 x}}{e ^{- 2 x} + c _{1}}, y = - \frac{e ^{- x^{2} - 2 x}}{e ^{- 2 x} + c _{1}}

\int (4 x^{2} - 8 x + 1) d x

n = 0 \sum \infty (1 - \frac{1}{n})^{n}

\frac{d x}{d t} = \frac{3}{x}

x \to 0 - lim ((\frac{1}{2})^{\frac{1}{x}})

x \to - 3 lim (8 x^{2})