(a) For what values of r does the function y = ex satisfy the differential equation 7y" + 34y' - 5y = 0? (Enter your answers as a comma-separated list.)r =(b) If r₁ and ₂ are the values of r that you found in part (a), show that every member of the family of functions y = ae^1× + be¹2× is also a solution.Let 1be the larger value and r₂ be the smaller value. We need to show that every member of the family of functions y = aer1× + ber2x 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 1x + be 2x.Substitute your values for ₁ and 7₂ 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) — 5f(x) =Der ₁x + ( [De²₂xle 2xTherefore, f(x) = ae 1x + be 2x is a solution to the differential equation 7y" + 34y' - 5y = 0.

We use the techniques of higher order differential equations to solve the given problem.

(a) For what values of r does the function y = ex satisfy the differential equation 7y" + 34y' - 5y = 0? (Enter your answers as a comma-separated list.) (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 2x is also a solution. Letr, be the larger value and r₂ 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 7y" + 34y' - 5y = 0. We must decide whether 7f"(x) + 34f'(x) - 5f(x) = 0 for f(x) = ae 1x + be 2x. Substitute your values for r₁ and ₂ 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) - 5f(x) = ₁²¹₁x + ( [ Derzx Therefore, f(x) = ae 1x + ber2x is a solution to the differential equation 7y" + 34y' - 5y = 0.

(a) For what values of r does the function y = ex satisfy the differential equation 7y" + 34y' - 5y = 0? (Enter your answers as a comma-separated list.) (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 2x is also a solution. Letr, be the larger value and r₂ 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 7y" + 34y' - 5y = 0. We must decide whether 7f"(x) + 34f'(x) - 5f(x) = 0 for f(x) = ae 1x + be 2x. Substitute your values for r₁ and ₂ 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) - 5f(x) = ₁²¹₁x + ( [ Derzx Therefore, f(x) = ae 1x + ber2x is a solution to the differential equation 7y" + 34y' - 5y = 0.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.CR: Chapter 11 Review

Problem 1CR

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