(dy)/(dx)=x^2sqrt(x-9)

Lösung

\frac{d y}{d x} = x^{2} x - 9

y = \frac{2}{7} (x - 9)^{\frac{7}{2}} + \frac{36}{5} (x - 9)^{\frac{5}{2}} + 54 (x - 9)^{\frac{3}{2}} + c_{1}

Schritte zur Lösung

\frac{d y}{d x} = x^{2} x - 9

Ersetze

\frac{d y}{d x}

mit

y^{'} (x)

y^{^{'}} (x) = x^{2} x - 9

Wenn

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

dann

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

y = \int x^{2} x - 9 d x

\int x^{2} x - 9 d x = \frac{2}{7} (x - 9)^{\frac{7}{2}} + \frac{36}{5} (x - 9)^{\frac{5}{2}} + 54 (x - 9)^{\frac{3}{2}} + c_{1}

y = \frac{2}{7} (x - 9)^{\frac{7}{2}} + \frac{36}{5} (x - 9)^{\frac{5}{2}} + 54 (x - 9)^{\frac{3}{2}} + c_{1}

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