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

The solution for (1+x^2)(dy)/(dx)-2xy=x^2+x^4 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

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

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}

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{\partial}{\partial x} (20 e^{5 x} y)

f (x) = ln (x^{2} - 1)

\frac{d}{d x} (\frac{x ^{2} - 6 x}{( x - 3 ) ^{2}})

\int \frac{3}{( x - 2 ) ^{2}} d x

(12, - 16), (- 9, 8)

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