What is the solution for y^'=y(xy^5+5) ?

The solution for y^'=y(xy^5+5) is y=\sqrt[5]{(125e^{25x})/(-25xe^{25x)+e^{25x}+c_{1}}}

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y^'=y(xy^5+5)

y^{^{'}} = y (x y^{5} + 5)

y = 5 \frac{125 e ^{25 x}}{- 25 x e ^{25 x} + e ^{25 x} + c _{1}}

Solution steps

y^{'} (x) = y (x y^{5} + 5)

Solve Bernoulli ODE:

y = 5 \frac{125 e ^{25 x}}{- 25 x e ^{25 x} + e ^{25 x} + c _{1}}

y = 5 \frac{125 e ^{25 x}}{- 25 x e ^{25 x} + e ^{25 x} + c _{1}}

\int sec^{4} (x) tan^{6} (x) d x

t^{2} (\frac{d y}{d t}) + y = 0

\frac{\partial}{\partial y} (y e^{z})

\frac{d y}{d x} + x y = x y^{- 3}

x \to - 4 π lim (1 + csc (x))

What is the solution for y^'=y(xy^5+5) ?
The solution for y^'=y(xy^5+5) is y=\sqrt[5]{(125e^{25x})/(-25xe^{25x)+e^{25x}+c_{1}}}