Để giải phương trình \(xy^2 + x^3 - 10y^3 = 0\), ta có thể làm như sau:

1. **Phân tích phương trình**:
\[
xy^2 + x^3 - 10y^3 = 0
\]

2. **Tách các hạng tử**:
\[
xy^2 + x^3 = 10y^3
\]

3. **Phân tích theo \(x\)**:
\[
x(y^2 + x^2) = 10y^3
\]

4. **Xét các trường hợp đặc biệt**:
- Nếu \(x = 0\):
\[
0 \cdot (y^2 + 0^2) = 10y^3 \implies 0 = 10y^3
\]
Điều này chỉ đúng khi \(y = 0\).

Vậy, một nghiệm là \((x, y) = (0, 0)\).

5. **Xét trường hợp \(x \neq 0\)**:
- Chia cả hai vế của phương trình cho \(x\):
\[
y^2 + x^2 = \frac{10y^3}{x}
\]
\[
y^2 + x^2 = 10y \cdot \frac{y^2}{x}
\]
\[
y^2 + x^2 = 10y \cdot \frac{y^2}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
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y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
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y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
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y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
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y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
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y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
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y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
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y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
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y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
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y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
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y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^2 = 10 \cdot \frac{y^3}{x}
\]
\[
y^2 + x^