What is the solution for (dy)/(dx)=x^2sqrt(x-9) ?

The solution for (dy)/(dx)=x^2sqrt(x-9) is y= 2/7 (x-9)^{7/2}+36/5 (x-9)^{5/2}+54(x-9)^{3/2}+c_{1}

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

\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}

Solution steps

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

Substitute

\frac{d y}{d x}

with

y^{'} (x)

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

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

then

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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What is the solution for (dy)/(dx)=x^2sqrt(x-9) ?
The solution for (dy)/(dx)=x^2sqrt(x-9) is y= 2/7 (x-9)^{7/2}+36/5 (x-9)^{5/2}+54(x-9)^{3/2}+c_{1}