What is the solution for (x^2+1)y^'+y^2+1=0,y(4)=e ?

The solution for (x^2+1)y^'+y^2+1=0,y(4)=e is y=tan(-arctan(x)+1.21828…+1.32581…)

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(x^2+1)y^'+y^2+1=0,y(4)=e

(x^{2} + 1) y^{^{'}} + y^{2} + 1 = 0, y (4) = e

y = tan (- arctan (x) + 1.21828 \dots + 1.32581 \dots)

Solution steps

(x^{2} + 1) y^{'} (x) + y^{2} + 1 = 0

Solve separable ODE:

y = tan (- arctan (x) + 1.21828 \dots + 1.32581 \dots)

y = tan (- arctan (x) + 1.21828 \dots + 1.32581 \dots)

\int \frac{1}{( sin ( x ) ) ^{2} ( cos ( x ) ) ^{4}} d x

\frac{d ^{4}}{d x ^{4}} (ln (x))

15 x^{\frac{1}{4}}

n = 0 \sum \infty (\frac{2}{3})^{n - 1}

What is the solution for (x^2+1)y^'+y^2+1=0,y(4)=e ?
The solution for (x^2+1)y^'+y^2+1=0,y(4)=e is y=tan(-arctan(x)+1.21828…+1.32581…)