Homework: 9.1 Basic Ideas Verify that the given function y is a solution of the differential equation that follows it. A

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Homework 9 1 Basic Ideas Verify That The Given Function Y Is A Solution Of The Differential Equation That Follows It A 1 (35.6 KiB) Viewed 43 times

Homework: 9.1 Basic Ideas Verify that the given function y is a solution of the differential equation that follows it. Assume that C is an arbitrary constant. 7t y(t) = Cet; y'(t)- 7y(t) = 0 7t Start by substituting y(t) = Cet into the second half of the equation. y' (t) + (-7 (Ce¹¹)); = 0 Next find the derivative of y(t) = Ce7t y'(t) = C7 e 7t Simplify the equation for the given function. Is the given function a solution for the differential equation? O A. Yes, because the given function equals 0, so the original function must satisfy the initial value problem. O B. No, because the given function does not equal 0, so the original function cannot satisfy the initial value problem. O C. Yes, because when y and y' are substituted into the equation, the result is a true statement. O D. No, because when y and y' are substituted into the equation, the result is not a true statement. Question 1, 9.1.7 Part 3 of 3 C HW Score: 0%, 0 of 8 points O Points: 0 of 1