What is the solution for (dy)/(dx)=(1+x)/(xy^5) ?

The solution for (dy)/(dx)=(1+x)/(xy^5) is y=\sqrt[6]{6ln(x)+6x+c_{1}},y=-\sqrt[6]{6ln(x)+6x+c_{1}}

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(dy)/(dx)=(1+x)/(xy^5)

\frac{d y}{d x} = \frac{1 + x}{x y ^{5}}

y = 6 6 ln (x) + 6 x + c_{1}, y = - 6 6 ln (x) + 6 x + c_{1}

Solution steps

\frac{d y}{d x} = \frac{1 + x}{x y ^{5}}

Solve separable ODE:

y = 6 6 ln (x) + 6 x + c_{1}, y = - 6 6 ln (x) + 6 x + c_{1}

y = 6 6 ln (x) + 6 x + c_{1}, y = - 6 6 ln (x) + 6 x + c_{1}

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

y^{^{'}} - e^{x} y = 0

y^{^{'}} y + x = 0

\frac{d x}{d t} + \frac{x}{100} = 100

\frac{d y}{d x} = (2 x y)

What is the solution for (dy)/(dx)=(1+x)/(xy^5) ?
The solution for (dy)/(dx)=(1+x)/(xy^5) is y=\sqrt[6]{6ln(x)+6x+c_{1}},y=-\sqrt[6]{6ln(x)+6x+c_{1}}