Definition:Linear First Order Ordinary Differential Equation
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Definition
A linear first order ordinary differential equation is a differential equation which is in (or can be manipulated into) the form:
- $\dfrac {dy}{dx} + P \left({x}\right) y = Q \left({x}\right)$
It is:
- Linear because both $\dfrac {dy}{dx}$ and $y$ appear to the first power, and do not occur multiplied together;
- First order because the highest derivative is $\dfrac {dy}{dx}$;
- Ordinary because there are no partial derivatives occurring in it.
Its general solution is:
- $\displaystyle y = e^{-\int P dx} \left({\int Q e^{\int P dx}dx + C}\right)$
where $C$ is an arbitrary constant.
Also see
