## Differential Equations and Linear Algebra (4th Edition)

$y=-\frac{1}{arctan(x)+C}$
Multiply both sides of the equation by $\frac{dx}{y^2}$ to separate variables. $$\frac{dx}{y^2}(\frac{dy}{dx}=\frac{y^2}{x^2+1})$$ $$\frac{dy}{y^2}=\frac{dx}{x^2+1}$$ Since each side is in terms of one variable, you can integrate each side. $$\int \frac{dy}{y^2}=\int \frac{dx}{x^2+1}$$ $$-\frac{1}{y}=arctan(x)+C$$ Solve for $y$. $$y=-\frac{1}{arctan(x)+C}$$