What is the solution for (dy)/(dx)=(1+x)/(xy^6),y(1)=5 ?

The solution for (dy)/(dx)=(1+x)/(xy^6),y(1)=5 is y=\sqrt[7]{7ln(x)+7x+78118}

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(dy)/(dx)=(1+x)/(xy^6),y(1)=5

\frac{d y}{d x} = \frac{1 + x}{x y ^{6}}, y (1) = 5

y = 7 7 ln (x) + 7 x + 78118

Solution steps

\frac{d y}{d x} = \frac{1 + x}{x y ^{6}}

Solve separable ODE:

y = 7 7 ln (x) + 7 x + 78118

y = 7 7 ln (x) + 7 x + 78118

\frac{d y}{d x} = 3 x^{2} + 3 x^{2} y^{2}

y^{^{'}} = cos (x) sec (y)

y^{^{'}} (x) = \frac{y cos ( x )}{1 + 3 y ^{3}}, y (0) = 1

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

(8 + x) \frac{d y}{d x} = 5 y

What is the solution for (dy)/(dx)=(1+x)/(xy^6),y(1)=5 ?
The solution for (dy)/(dx)=(1+x)/(xy^6),y(1)=5 is y=\sqrt[7]{7ln(x)+7x+78118}