X (a) For what values of r does the function y = e satisfy the differential equation 7y" + 34y' - 5y = 0? (Enter your answers as a comma-separated list.) r = (b) If r, and r2 are the values of r that you found in part (a), show that every member of the family of functions y = ae 1x + be 2 is also a solution. => Let r be the larger value and r be the smaller value. We need to show that every member of the family of functions y = ae 1* + be 2 is a solution of the differential equation 7y" + 34y' - 5y = 0. We must decide whether 7f"(x) + 34f'(x) - 5f(x) = 0 for f(x) = ae 1* + 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. 7f(x)+34f(x) - 5/(x) = + Therefore, f(x) = ae 1x + be 2 is a solution to the differential equation 7y" + 34y' - 5y = 0. Need Help? Read It Watch It Master It