# Differential Equation Probability

**Discrete Mathematics**Level 4

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