What is the solution for (dy)/(dx)=xsqrt(x-18) ?

The solution for (dy)/(dx)=xsqrt(x-18) is y= 2/5 (x-18)^{5/2}+12(x-18)^{3/2}+c_{1}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(dy)/(dx)=xsqrt(x-18)

\frac{d y}{d x} = x x - 18

y = \frac{2}{5} (x - 18)^{\frac{5}{2}} + 12 (x - 18)^{\frac{3}{2}} + c_{1}

Solution steps

\frac{d y}{d x} = x x - 18

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = x x - 18

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

then

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

y = \int x x - 18 d x

\int x x - 18 d x = \frac{2}{5} (x - 18)^{\frac{5}{2}} + 12 (x - 18)^{\frac{3}{2}} + c_{1}

y = \frac{2}{5} (x - 18)^{\frac{5}{2}} + 12 (x - 18)^{\frac{3}{2}} + c_{1}

What is the solution for (dy)/(dx)=xsqrt(x-18) ?
The solution for (dy)/(dx)=xsqrt(x-18) is y= 2/5 (x-18)^{5/2}+12(x-18)^{3/2}+c_{1}