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Consider a linear ordinary differential equation: $\frac{dy}{dx}+p\left ( x \right )y=r\left ( x \right )$. Functions $p\left ( x \right )$ and $r\left ( x \right )$ are defined and have a continuous first derivative. The integrating factor of this equation is non-zero. Multiplying this equation by its integrating factor converts this into a:

- Homogeneous differential equation
- Non-linear differential equation
- Second order differential equation
- Exact differential equation