What is the solution for dx=x^5ydy ?

The solution for dx=x^5ydy is y=(sqrt(4c_{1)x^4-1})/(sqrt(2)x^2),y=-(sqrt(4c_{1)x^4-1})/(sqrt(2)x^2)

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dx=x^5ydy

d x = x^{5} y d y

y = \frac{4 c _{1} x ^{4} - 1}{2 x ^{2}}, y = - \frac{4 c _{1} x ^{4} - 1}{2 x ^{2}}

Solution steps

d x = x^{5} y d y

Solve separable ODE:

y = \frac{4 c _{1} x ^{4} - 1}{2 x ^{2}}, y = - \frac{4 c _{1} x ^{4} - 1}{2 x ^{2}}

y = \frac{4 c _{1} x ^{4} - 1}{2 x ^{2}}, y = - \frac{4 c _{1} x ^{4} - 1}{2 x ^{2}}

y^{^{'}} = 1 + x + y^{2} + y^{2} x

\frac{d x}{d t} = 5000 + 0.04 x, x = 18000, t = 0

y + x \frac{d y}{d x} = 2 x^{2} y \frac{d y}{d x} + 2 x y^{2}

\frac{d y}{d t} = 3 - 0.04 y

What is the solution for dx=x^5ydy ?
The solution for dx=x^5ydy is y=(sqrt(4c_{1)x^4-1})/(sqrt(2)x^2),y=-(sqrt(4c_{1)x^4-1})/(sqrt(2)x^2)