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(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 r₂ are the values of r that you found in part (a), show that every member of the family of functions y = ae1* + be 2* is 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 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) = ae1* + be 2*. Substitute your values for ₁ 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) = e²₁x + ( [ 1x Derzx Therefore, f(x) = ae1* + be 2* 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.) 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 functions y = ae1* + be 2* is 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 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) = ae1* + be 2*. Substitute your values for ₁ 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) = e²₁x + ( [ 1x Derzx Therefore, f(x) = ae1* + be 2* is a solution to the differential equation 7y" + 34y' - 5y = 0.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(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 = ae¹¹× + be^2× is also a solution. 1 Let ₁ be the larger value and r₂ be the smaller value. We need to show that every member of the family of functions y = 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 r₂ 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) ₁²₁x + ( [ Therefore, f(x) = ae^1× + be^2× is a solution to the differential equation 7y" + 34y' - 5y = 0. er 2x ae1x + be 2* is a solution of the differential
Transcribed Image Text:(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 = ae¹¹× + be^2× is also a solution. 1 Let ₁ be the larger value and r₂ be the smaller value. We need to show that every member of the family of functions y = 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 r₂ 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) ₁²₁x + ( [ Therefore, f(x) = ae^1× + be^2× is a solution to the differential equation 7y" + 34y' - 5y = 0. er 2x ae1x + be 2* is a solution of the differential
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