(a)For what values of r does the function y = erx satisfy the differential equation5y+24y5y =0?(Enter your answers as a comma-separated list.)r =(b)If r1 and r2 are the values of r that you found in part (a), show that every member of the family of functionsy = aer1x + ber2xis also a solution.Let r1 be the larger value and r2 be the smaller value. We need to show that every member of the family of functionsy = aer1x + ber2xis a solution of the differential equation5y+24y5y =0.We must decide whether5f(x)+24f(x)5f(x)=0forf(x)= aer1x + ber2x.Substitute your values forr1 and r2intof(x),then findf'(x) and f''(x).We havef(x)=andf(x)=.Substituting and combining like terms, we get the following.5f(x)+24f(x)5f(x)=er1x +er2xTherefore,f(x)= aer1x + ber2xis a solution to the differential equation5y+24y5y =0.