What is the solution for (1+x^2)(dy)/(dx)-(2xy+x^2+x^4)=0 ?

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

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(1+x^2)(dy)/(dx)-(2xy+x^2+x^4)=0

(1 + x^{2}) \frac{d y}{d x} - (2 x y + x^{2} + x^{4}) = 0

y = x (1 + x^{2}) - arctan (x) (1 + x^{2}) + c_{1} (1 + x^{2})

Solution steps

(1 + x^{2}) \frac{d y}{d x} - (2 x y + x^{2} + x^{4}) = 0

Solve linear ODE:

y = x (1 + x^{2}) - arctan (x) (1 + x^{2}) + c_{1} (1 + x^{2})

y = x (1 + x^{2}) - arctan (x) (1 + x^{2}) + c_{1} (1 + x^{2})

\frac{d x}{d t} - \frac{2}{3 t} x = 4 t x^{- 5}

\frac{d}{d x} (x^{2} (e^{x} - 1))

x \to \frac{π}{2} lim (2 sec (x))

\int_{1}^{2} 3 \frac{ln ( x )}{x ^{2}} d x

x \to 4 lim (x + 3)

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