Question

Determine the solution of the following differential equation:

xxy '= 1 + y^2

Answer 1

$$xy '= 1 + y^2$$

$$\dfrac{dy}{1+y^2}=\dfrac{dx}{x}$$

Integrate

$$\int \dfrac{dy}{1+y^2}=\int\dfrac{dx}{x}$$

$$\tan^{-1}y=\ln(|x|)+C$$

$$y=\tan(\ln(|x|)+C)$$