# Differential Equation Probability

Three numbers are chosen at random without replacement from $$\{1,2,3,......,9\}$$. Probability that their minimum is equal to the order of differential equation $$\large{\color{blue}{x^{3}\frac{d^{3}y}{dx^{3}}+x^{2}\frac{d^{2}y}{dx^{2}}+x\frac{dy}{dx}+y=0}}$$ given that their maximum is equal to degree of differential equation $$\large{\color{blue}{{ y }^{ 2 }=2\frac { dy }{ dx } \left( x+\sqrt [ 5 ]{ \frac { dy }{ dx } } \right)}}$$ is

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