What is the solution for (x^2+1)(dy)/(dx)+6x(y-1)=0 ?

The solution for (x^2+1)(dy)/(dx)+6x(y-1)=0 is y=(c_{1})/(x^6+3x^4+3x^2+1)+1

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(x^2+1)(dy)/(dx)+6x(y-1)=0

(x^{2} + 1) \frac{d y}{d x} + 6 x (y - 1) = 0

y = \frac{c _{1}}{x ^{6} + 3 x ^{4} + 3 x ^{2} + 1} + 1

Solution steps

(x^{2} + 1) \frac{d y}{d x} + 6 x (y - 1) = 0

Solve separable ODE:

y = \frac{c _{1}}{x ^{6} + 3 x ^{4} + 3 x ^{2} + 1} + 1

y = \frac{c _{1}}{x ^{6} + 3 x ^{4} + 3 x ^{2} + 1} + 1

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

y^{^{'}} + \frac{y}{x} = x^{- 4}

s (t) = 14 + 15 sin (14 π t)

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

sin^{2} (π t)

What is the solution for (x^2+1)(dy)/(dx)+6x(y-1)=0 ?
The solution for (x^2+1)(dy)/(dx)+6x(y-1)=0 is y=(c_{1})/(x^6+3x^4+3x^2+1)+1