Variable Separable

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The solution of x dy - y dx = 0 is

RankGuru · Accepted Answer

1. **Rearrange Equation**: $x \, dy = y \, dx$.
2. **Group Variables**: Divide by $xy$ (assuming $x, y 
eq 0$).
   - $\frac{dy}{y} = \frac{dx}{x}$
3. **Integrate**:
   - $\ln y = \ln x + \ln C$
   - $\ln y = \ln (Cx)$
4. **Extract Variables**: $y = Cx$.
- Note: This represents a family of straight lines passing through the origin.

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Variable Separable

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