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Q.1 A. It is given that the functions of x, f and g, satisfy the following coupled first order differential equations. f'(x)- 5f(x) 3g(x) and g'(x) + 4g(x) =-6f(x) %3D a) Show that f"(x)- f'(x) - 2f(x) = 0 b) Given further that f(0) =1 and g(0) = 3, solve the differential equation of %3! part (a) to obtain simplified expressions for f(x) and g(x). B. By using one of the test methods, test the convergence of the following series: Σ 3" + 4" 2n + 3n n=1

Q.1 A. It is given that the functions of x, f and g, satisfy the following coupled first order differential equations. f'(x)- 5f(x) 3g(x) and g'(x) + 4g(x) =-6f(x) %3D a) Show that f"(x)- f'(x) - 2f(x) = 0 b) Given further that f(0) =1 and g(0) = 3, solve the differential equation of %3! part (a) to obtain simplified expressions for f(x) and g(x). B. By using one of the test methods, test the convergence of the following series: Σ 3" + 4" 2n + 3n n=1

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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Q.1 A. It is given that the functions of x, f and g, satisfy the following coupled first order differential equations. r(x)- 5f(x) 3g(x) and g'(x) + 4g(x) = -6/(x) a) Show that f"(x) - f'(x) - 2f(x) = 0 b) Given further that f(0) =1 and g(0) = 3, solve the differential equation of %3D part (a) to obtain simplified expressions for f(x) and g(x). B. By using one of the test methods, test the convergence of the following series: 8. 3" + 4" 2n + 3n n=1
Transcribed Image Text:Q.1 A. It is given that the functions of x, f and g, satisfy the following coupled first order differential equations. r(x)- 5f(x) 3g(x) and g'(x) + 4g(x) = -6/(x) a) Show that f"(x) - f'(x) - 2f(x) = 0 b) Given further that f(0) =1 and g(0) = 3, solve the differential equation of %3D part (a) to obtain simplified expressions for f(x) and g(x). B. By using one of the test methods, test the convergence of the following series: 8. 3" + 4" 2n + 3n n=1
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