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Beliebt Rechnen >

(dy)/(dx)= 2/(sqrt(16-x^2))

Lösung

\frac{d y}{d x} = \frac{2}{16 - x ^{2}}

Lösung

y = 2 arcsin (\frac{1}{4} x) + c_{1}

Schritte zur Lösung

\frac{d y}{d x} = \frac{2}{16 - x ^{2}}

Ersetze

\frac{d y}{d x}

mit

y^{'} (x)

y^{^{'}} (x) = \frac{2}{16 - x ^{2}}

Wenn

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

dann

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

y = \int \frac{2}{16 - x ^{2}} d x

\int \frac{2}{16 - x ^{2}} d x = 2 arcsin (\frac{1}{4} x) + c_{1}

y = 2 arcsin (\frac{1}{4} x) + c_{1}

Graph

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(dy)/(dx)=-(5y)/(50+x)

\frac{d y}{d x} = - \frac{5 y}{50 + x}

xy^'=5y-x,y(1)=1

x y^{^{'}} = 5 y - x, y (1) = 1