(a) For what values of r does the function y = ex satisfy the differential equation 5y" + 34y' - 7y = 0? (Enter your answers as a comma-separated list.) r (b) If r and r are the values of r that you found in part (a), show that every member of the family of functions y = ae1* + bez is also a solution. be the larger value and r be the smaller value. We need to show that every member of the family of functions y = ae1* + be 2* is a solution of the differential equation 5y" + 34y' - 7y = 0. Let 1 We must decide whether 5f"(x) + 34f'(x) 7f(x) = 0 for f(x) = ae1* + be^2*. Substitute your values for r and r into f(x), then find f'(x) and f'(x). We have f'(x) = and f(x) = Substituting and combining like terms, we get the following. 5f"(x) + 34f'(x) = f(x) = 1) 1x + e2x Therefore, f(x)=ae 1x + be 2* is a solution to the differential equation 5y + 34y' 7y = 0.