## Question

###### Consider the ODEy" + Bxy' +y = 0(1)Find a (constant) value of B so that at least one non-zero solution of (1) is just a (finite) polynomial, instead of an infinite series. Actually, there are an infinite number of choices for this constant B that give finite, nonzero polynomial solutions. So to pin things down, choose the value of B that gives a polynomial of 3rd degree. Finally, to completely pin things down, make sure the coefficient of in your solution is -1 , Find this solution: Ch

Consider the ODE y" + Bxy' +y = 0 (1) Find a (constant) value of B so that at least one non-zero solution of (1) is just a (finite) polynomial, instead of an infinite series. Actually, there are an infinite number of choices for this constant B that give finite, nonzero polynomial solutions. So to pin things down, choose the value of B that gives a polynomial of 3rd degree. Finally, to completely pin things down, make sure the coefficient of in your solution is -1 , Find this solution: Check to make sure your proposed solution actually solves (1) for the indicated value of B _ What is B ?

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