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Beliebt Rechnen >

(dy)/(dx)= 1/(2x(7-x))

Lösung

\frac{d y}{d x} = \frac{1}{2 x ( 7 - x )}

Lösung

y = \frac{1}{2} (\frac{1}{7} ln (x) - \frac{1}{7} ln (x - 7)) + c_{1}

Schritte zur Lösung

\frac{d y}{d x} = \frac{1}{2 x ( 7 - x )}

Ersetze

\frac{d y}{d x}

mit

y^{'} (x)

y^{^{'}} (x) = \frac{1}{2 x ( 7 - x )}

Wenn

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

dann

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

y = \int \frac{1}{2 x ( 7 - x )} d x

\int \frac{1}{2 x ( 7 - x )} d x = \frac{1}{2} (\frac{1}{7} ln (x) - \frac{1}{7} ln (x - 7)) + c_{1}

y = \frac{1}{2} (\frac{1}{7} ln (x) - \frac{1}{7} ln (x - 7)) + c_{1}

Graph

Beliebte Beispiele

y^'-3x^2y=12x^2

y^{^{'}} - 3 x^{2} y = 12 x^{2}

derivative (5x^2-8x)e^x

d er i v a t i v e (5 x^{2} - 8 x) e^{x}

integral of 1/(1-4x^2)

\int \frac{1}{1 - 4 x ^{2}} d x

tangent f(x)=-5-3x^2,-53,\at x=4

t an g e n t f (x) = - 5 - 3 x^{2}, - 53, at x = 4

steigung (-3.2)(7.6)

s l o p e (- 3.2) (7.6)