= Implicit differential equation
{title2=$F(x,y,y')=0$}
An implicit <ordinary differential equation> relates the <derivative> to the independent and dependent <variables> without requiring it to be explicitly isolated. For example $y y'=1$ is meaningful at every pair $(x,y)$ as an equation, but no differentiable <solution of a differential equation> can pass through $y=0$: its left side would vanish there. Dividing by $y$ gives $y'=1/y$ only on the domain $y\ne0$. Conversely multiplying an explicit equation by a vanishing denominator can introduce points where the original equation was undefined. A solution of the multiplied equation at such a point need not solve the original <initial value problem>.
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