What is the solution for (dy)/(dx)=xsqrt(x-15) ?

The solution for (dy)/(dx)=xsqrt(x-15) is y= 2/5 (x-15)^{5/2}+10(x-15)^{3/2}+c_{1}

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

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

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

Solution steps

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

Substitute

\frac{d y}{d x}

with

y^{'} (x)

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

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

then

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}

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\int \frac{1}{x 9 + 4 x ^{2}} d x

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What is the solution for (dy)/(dx)=xsqrt(x-15) ?
The solution for (dy)/(dx)=xsqrt(x-15) is y= 2/5 (x-15)^{5/2}+10(x-15)^{3/2}+c_{1}