What is the solution for (dy)/(dx)=xsqrt(x-27) ?

The solution for (dy)/(dx)=xsqrt(x-27) is y= 2/5 (x-27)^{5/2}+18(x-27)^{3/2}+c_{1}

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(dy)/(dx)=xsqrt(x-27)

\frac{d y}{d x} = x x - 27

y = \frac{2}{5} (x - 27)^{\frac{5}{2}} + 18 (x - 27)^{\frac{3}{2}} + c_{1}

Solution steps

\frac{d y}{d x} = x x - 27

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = x x - 27

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

then

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

y = \int x x - 27 d x

\int x x - 27 d x = \frac{2}{5} (x - 27)^{\frac{5}{2}} + 18 (x - 27)^{\frac{3}{2}} + c_{1}

y = \frac{2}{5} (x - 27)^{\frac{5}{2}} + 18 (x - 27)^{\frac{3}{2}} + c_{1}

What is the solution for (dy)/(dx)=xsqrt(x-27) ?
The solution for (dy)/(dx)=xsqrt(x-27) is y= 2/5 (x-27)^{5/2}+18(x-27)^{3/2}+c_{1}