What is the solution for (dy)/(dx)=6x^3sqrt(y),y>0 ?

The solution for (dy)/(dx)=6x^3sqrt(y),y>0 is y=(9x^8}{16}+\frac{3c_{1}x^4)/4+(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)=6x^3sqrt(y),y>0

\frac{d y}{d x} = 6 x^{3} y, y > 0

y = \frac{9 x ^{8}}{16} + \frac{3 c _{1} x ^{4}}{4} + \frac{c _{1}^{2}}{4}

Solution steps

\frac{d y}{d x} = 6 x^{3} y

Solve separable ODE:

y = \frac{9 x ^{8}}{16} + \frac{3 c _{1} x ^{4}}{4} + \frac{c _{1}^{2}}{4}

y = \frac{9 x ^{8}}{16} + \frac{3 c _{1} x ^{4}}{4} + \frac{c _{1}^{2}}{4}

What is the solution for (dy)/(dx)=6x^3sqrt(y),y>0 ?
The solution for (dy)/(dx)=6x^3sqrt(y),y>0 is y=(9x^8}{16}+\frac{3c_{1}x^4)/4+(c_{1}^2)/4