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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

2 \frac{d y}{d t} + 4 y = 6

y^{^{'}} = 0.5 y (1 - \frac{y}{10000})

d v = 4 π r^{2} d r

y^{^{'}} - 2 y = 6

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