What is the solution for (dy)/(dx)=8x^4(6+y^2)^{3/2} ?

The solution for (dy)/(dx)=8x^4(6+y^2)^{3/2} is

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(dy)/(dx)=8x^4(6+y^2)^{3/2}

\frac{d y}{d x} = 8 x^{4} (6 + y^{2})^{\frac{3}{2}}

y = \frac{6 6 - 64 x ^{10} - 80 c _{1} x ^{5} - 25 c _{1}^{2}}{- 25 + 900 c _{1}^{2} + 2880 c _{1} x ^{5} + 2304 x ^{10}}, y = - \frac{6 6 - 64 x ^{10} - 80 c _{1} x ^{5} - 25 c _{1}^{2}}{- 25 + 900 c _{1}^{2} + 2880 c _{1} x ^{5} + 2304 x ^{10}}

Solution steps

\frac{d y}{d x} = 8 x^{4} (6 + y^{2})^{\frac{3}{2}}

Solve separable ODE:

y = \frac{6 6 - 64 x ^{10} - 80 c _{1} x ^{5} - 25 c _{1}^{2}}{- 25 + 900 c _{1}^{2} + 2880 c _{1} x ^{5} + 2304 x ^{10}}, y = - \frac{6 6 - 64 x ^{10} - 80 c _{1} x ^{5} - 25 c _{1}^{2}}{- 25 + 900 c _{1}^{2} + 2880 c _{1} x ^{5} + 2304 x ^{10}}

y = \frac{6 6 - 64 x ^{10} - 80 c _{1} x ^{5} - 25 c _{1}^{2}}{- 25 + 900 c _{1}^{2} + 2880 c _{1} x ^{5} + 2304 x ^{10}}, y = - \frac{6 6 - 64 x ^{10} - 80 c _{1} x ^{5} - 25 c _{1}^{2}}{- 25 + 900 c _{1}^{2} + 2880 c _{1} x ^{5} + 2304 x ^{10}}

What is the solution for (dy)/(dx)=8x^4(6+y^2)^{3/2} ?
The solution for (dy)/(dx)=8x^4(6+y^2)^{3/2} is