What is the solution for (x^2+1)(dy)/(dx)+8x(y-1)=0,y(0)=2 ?

The solution for (x^2+1)(dy)/(dx)+8x(y-1)=0,y(0)=2 is y= 1/(x^8+4x^6+6x^4+4x^2+1)+1

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(x^2+1)(dy)/(dx)+8x(y-1)=0,y(0)=2

(x^{2} + 1) \frac{d y}{d x} + 8 x (y - 1) = 0, y (0) = 2

y = \frac{1}{x ^{8} + 4 x ^{6} + 6 x ^{4} + 4 x ^{2} + 1} + 1

Solution steps

(x^{2} + 1) \frac{d y}{d x} + 8 x (y - 1) = 0

Solve separable ODE:

y = \frac{1}{x ^{8} + 4 x ^{6} + 6 x ^{4} + 4 x ^{2} + 1} + 1

y = \frac{1}{x ^{8} + 4 x ^{6} + 6 x ^{4} + 4 x ^{2} + 1} + 1

\int \frac{1}{8 - x ^{2}} d x

x^{2} - 4 x + 6

\int \frac{1}{y ^{\frac{11}{5}}} d y

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

\int - 4 x^{6} - 5 x^{5} - 2 x^{2} + 5 - e^{x} d x

What is the solution for (x^2+1)(dy)/(dx)+8x(y-1)=0,y(0)=2 ?
The solution for (x^2+1)(dy)/(dx)+8x(y-1)=0,y(0)=2 is y= 1/(x^8+4x^6+6x^4+4x^2+1)+1