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

解

\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}

解答ステップ

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

代用

\frac{d y}{d x}

と

y^{'} (x)

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

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

であれば

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}