What is the solution for x^5*y^'+y^5=0 ?

The solution for x^5*y^'+y^5=0 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^5*y^'+y^5=0

x^{5} \cdot y^{^{'}} + y^{5} = 0

Solution steps

x^{5} \cdot y^{'} (x) + y^{5} = 0

Solve separable ODE:

\frac{d x}{1 + x ^{2}} + \frac{d y}{1 + y ^{2}} = 0

x cos (y) \frac{d y}{d x} - sin (y) = 0

x^{(- 2)} y^{(- 5)} d x + x^{(- 3)} y^{(- 4)} d y = 0

y^{^{'}} + x - x^{2} \cdot y = x - x^{2}

y^{^{'}} x + 4 y = 1

What is the solution for x^5*y^'+y^5=0 ?
The solution for x^5*y^'+y^5=0 is y=\sqrt[4]{-(x^4)/(1+4c_{1)x^4}},y=-\sqrt[4]{-(x^4)/(1+4c_{1)x^4}}