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

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

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(dy)/(dx)= 1/(y+x^2y)

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{d y}{d x} = 6 - \frac{y}{20}

y^{^{'}} + 3 y = 1, 3 sin (2 t) y (0) = 6

\frac{d y}{d x} \frac{1}{x} + \frac{1}{y} = 1

y^{^{'}} = \frac{x ^{2}}{- 4 y}

y^{^{'}} = \frac{( 3 x ^{2} - 1 )}{( 3 + 2 y )}, y (1) = 1

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