What is the solution for x^5dy=-y^5dx ?

The solution for x^5dy=-y^5dx is y=\sqrt[4]{-(x^4)/(1+4c_{1)x^4}},y=-\sqrt[4]{-(x^4)/(1+4c_{1)x^4}}

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x^5dy=-y^5dx

x^{5} d y = - y^{5} d x

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

Solution steps

x^{5} d y = - y^{5} d x

Solve separable ODE:

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

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

y^{^{'}} + 4 y = 11, y (0) = 1

\frac{d x}{d t} = \frac{4}{x e ^{t + 6 x}}

y^{^{'}} = \frac{( 3 x ^{2} )}{2 y}

\frac{d}{d x} (4 x^{3} + 2 y^{5}) = 6

\frac{d y}{d x} = (x - 1) (y + 1)

What is the solution for x^5dy=-y^5dx ?
The solution for x^5dy=-y^5dx is y=\sqrt[4]{-(x^4)/(1+4c_{1)x^4}},y=-\sqrt[4]{-(x^4)/(1+4c_{1)x^4}}