Problem 12.(15 points)In this problem you will solve the differential equation(x2+2)y''+10xy'-y=0(1) By analyzing the singular points of the differential equation, we know that a series solution of the form y=n=0cnxn for the differential equation will converge at least on the interval(2) Substituting y=n=0cnxn into (x2+2)y''+10xy'-y=0, you get that(x2+2),??n=-,c-x-+10xMultiplying the coefficients in x through the sums??n=?,c-x-,+??n=?-cReindex the sums??n=?-c-x-,+??n=?-cFinally combine the sumsqquadqquadqquad