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Beliebt Rechnen >

(dy)/(dx)=xsqrt(x-15)

Lösung

\frac{d y}{d x} = x x - 15

Lösung

y = \frac{2}{5} (x - 15)^{\frac{5}{2}} + 10 (x - 15)^{\frac{3}{2}} + c_{1}

Schritte zur Lösung

\frac{d y}{d x} = x x - 15

Ersetze

\frac{d y}{d x}

mit

y^{'} (x)

y^{^{'}} (x) = x x - 15

Wenn

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

dann

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

y = \int x x - 15 d x

\int x x - 15 d x = \frac{2}{5} (x - 15)^{\frac{5}{2}} + 10 (x - 15)^{\frac{3}{2}} + c_{1}

y = \frac{2}{5} (x - 15)^{\frac{5}{2}} + 10 (x - 15)^{\frac{3}{2}} + c_{1}

Graph

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\frac{d}{d x} y + y = 7

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