The general solution of the differential equation $(x^2 - yx^2)dy + (y^2 + x^2y^2)dx = 0$ is:

The differential equation is $(x^2 - yx^2)dy + (y^2 + x^2y^2)dx = 0$

Factor out common terms:

$x^2(1 - y)dy + y^2(1 + x^2)dx = 0$

---

Rearranging:

$x^2(1 - y)dy = -y^2(1 + x^2)dx$

Dividing both sides by $x^2y^2$:

$\frac{(1 - y)dy}{y^2} = -\frac{(1 + x^2)dx}{x^2}$

---

Expanding the left side:

$\frac{(1 - y)dy}{y^2} = \frac{dy}{y^2} - \frac{dy}{y}$

Expanding the right side:

$-\frac{(1 + x^2)dx}{x^2} = -\frac{dx}{x^2} - dx$

The equation becomes:

$\frac{dy}{y^2} - \frac{dy}{y} = -\frac{dx}{x^2} - dx$

---

Integrating both sides:

$\int \frac{dy}{y^2} - \int \frac{dy}{y} = -\int \frac{dx}{x^2} - \int dx$

$-\frac{1}{y} - \log_e|y| = \frac{1}{x} - x + c$

---

Multiplying by $-1$:

$\frac{1}{y} + \log_e|y| = -\frac{1}{x} + x - c$

Replacing $-c$ with $c$:

$\log_e|y| + \frac{1}{y} = -\frac{1}{x} + x + c$

Rearranging:

$\log_e|y| + \frac{1}{x} + \frac{1}{y} - x = c$