What is the solution for (dy)/(dx)=xsqrt(x-6) ?

The solution for (dy)/(dx)=xsqrt(x-6) is y= 2/5 (x-6)^{5/2}+4(x-6)^{3/2}+c_{1}

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(dy)/(dx)=xsqrt(x-6)

\frac{d y}{d x} = x x - 6

y = \frac{2}{5} (x - 6)^{\frac{5}{2}} + 4 (x - 6)^{\frac{3}{2}} + c_{1}

Solution steps

\frac{d y}{d x} = x x - 6

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = x x - 6

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

then

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

y = \int x x - 6 d x

\int x x - 6 d x = \frac{2}{5} (x - 6)^{\frac{5}{2}} + 4 (x - 6)^{\frac{3}{2}} + c_{1}

y = \frac{2}{5} (x - 6)^{\frac{5}{2}} + 4 (x - 6)^{\frac{3}{2}} + c_{1}

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What is the solution for (dy)/(dx)=xsqrt(x-6) ?
The solution for (dy)/(dx)=xsqrt(x-6) is y= 2/5 (x-6)^{5/2}+4(x-6)^{3/2}+c_{1}