What is the solution for (dy)/(dx)=20sqrt(xy) ?

The solution for (dy)/(dx)=20sqrt(xy) is y=(400x^3)/9+(20c_{1}x^{3/2})/3+(c_{1}^2)/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(dy)/(dx)=20sqrt(xy)

\frac{d y}{d x} = 20 x y

y = \frac{400 x ^{3}}{9} + \frac{20 c _{1} x ^{\frac{3}{2}}}{3} + \frac{c _{1}^{2}}{4}

Solution steps

\frac{d y}{d x} = 20 x y

Solve separable ODE:

y = \frac{400 x ^{3}}{9} + \frac{20 c _{1} x ^{\frac{3}{2}}}{3} + \frac{c _{1}^{2}}{4}

y = \frac{400 x ^{3}}{9} + \frac{20 c _{1} x ^{\frac{3}{2}}}{3} + \frac{c _{1}^{2}}{4}

What is the solution for (dy)/(dx)=20sqrt(xy) ?
The solution for (dy)/(dx)=20sqrt(xy) is y=(400x^3)/9+(20c_{1}x^{3/2})/3+(c_{1}^2)/4