Find the particular solution of the following differential equation: dx/dy = 1 + x² + y² + x²y², given that y = 1 when x = 0.

dx/dy = 1 + x² + y² + x²y²
∴ dx/dy = (1 + x²)(1 + y²)
∴ dx/(1 + x²) = (1 + y²)dy
Integrating both sides, we get
tan⁻¹x = y + y³/3 + c, where c is a constant of integration, whose value can be found out by substituting the given values.
Substituting y = 1 when x = 0, we get
tan⁻¹0 = 1 + 1³/3 + c
∴ 0 = c + 4/3
⇒ c = -4/3
Thus, the solution can be written as
tan⁻¹x = y + y³/3 - 4/3
i.e. 3tan⁻¹x = 3y + y³ - 4