What is the solution for (dy)/(dx)=2xsqrt(x-7) ?

The solution for (dy)/(dx)=2xsqrt(x-7) is y=2(2/5 (x-7)^{5/2}+14/3 (x-7)^{3/2})+c_{1}

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(dy)/(dx)=2xsqrt(x-7)

\frac{d y}{d x} = 2 x x - 7

y = 2 (\frac{2}{5} (x - 7)^{\frac{5}{2}} + \frac{14}{3} (x - 7)^{\frac{3}{2}}) + c_{1}

Solution steps

\frac{d y}{d x} = 2 x x - 7

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = 2 x x - 7

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

then

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

y = \int 2 x x - 7 d x

\int 2 x x - 7 d x = 2 (\frac{2}{5} (x - 7)^{\frac{5}{2}} + \frac{14}{3} (x - 7)^{\frac{3}{2}}) + c_{1}

y = 2 (\frac{2}{5} (x - 7)^{\frac{5}{2}} + \frac{14}{3} (x - 7)^{\frac{3}{2}}) + c_{1}

x \to - 2 lim (\frac{3 x}{x + 2})

\int 5 x^{\frac{3}{7}} d x

x^{2} - 12

f (x) = (\frac{2 x}{3} x + \frac{3}{2} x) 2

\frac{d}{d x} (arccosh (sec (x)))

What is the solution for (dy)/(dx)=2xsqrt(x-7) ?
The solution for (dy)/(dx)=2xsqrt(x-7) is y=2(2/5 (x-7)^{5/2}+14/3 (x-7)^{3/2})+c_{1}