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Beliebt Rechnen >

a^2dx=xsqrt(x^2-a^2)dy

Lösung

a^{2} d x = x x^{2} - a^{2} d y

Lösung

y = a arctan (\frac{x ^{2} - a ^{2}}{a}) + c_{1}

Schritte zur Lösung

a^{2} d x = x x^{2} - a^{2} d y

Lass

y

die abhängige Variable sein. Teile durch

d x

:

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

Ersetze

\frac{d y}{d x}

mit

y^{'} (x)

a^{2} = x x^{2} - a^{2} y^{^{'}} (x)

Isoliere

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

Wenn

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

dann

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

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

\int \frac{a ^{2}}{x x ^{2} - a ^{2}} d x = a arctan (\frac{x ^{2} - a ^{2}}{a}) + c_{1}

y = a arctan (\frac{x ^{2} - a ^{2}}{a}) + c_{1}

Graph

Beliebte Beispiele

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a re a y = 3 x, y = 9, y = \frac{1}{4} x^{2}

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\int (x^{3} + 2)^{8} 3 x^{2} d x

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