(x+1)(dy)/(dx)=(x+6)

Lösung

(x + 1) \frac{d y}{d x} = (x + 6)

y = 5 ln (x + 1) + x + c_{1}

Schritte zur Lösung

(x + 1) \frac{d y}{d x} = (x + 6)

Ersetze

\frac{d y}{d x}

mit

y^{'} (x)

(x + 1) y^{^{'}} (x) = (x + 6)

Isoliere

y^{'} (x) : y^{'} (x) = \frac{x + 6}{x + 1}

Wenn

f^{^{'}} (x) = g (x)

dann

f (x) = \int g (x) d x

y = \int \frac{x + 6}{x + 1} d x

\int \frac{x + 6}{x + 1} d x = 5 ln (x + 1) + x + c_{1}

y = 5 ln (x + 1) + x + c_{1}

x \to 3 lim (\frac{x}{2} + 1)

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