(a) It is given that y=f(x) is the solution of the differential equation d'y dy +5+6y=3x² +5 dr dx² Such that f(0) = 0 and f'(0) = 1 (i) Without solving the differential equation, show that f(0) = -6 and find the value of f(*)(0). (ii) Hence find the first three non-zero terms in the expansion, in ascending powers of x, of f(x). (b) Find the general solution of the differential equation d'y dy dr² dr +5- +6y=3x² +5
(a) It is given that y=f(x) is the solution of the differential equation d'y dy +5+6y=3x² +5 dr dx² Such that f(0) = 0 and f'(0) = 1 (i) Without solving the differential equation, show that f(0) = -6 and find the value of f(*)(0). (ii) Hence find the first three non-zero terms in the expansion, in ascending powers of x, of f(x). (b) Find the general solution of the differential equation d'y dy dr² dr +5- +6y=3x² +5
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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Transcribed Image Text:(a) It is given that y=f(x) is the solution of the differential equation
d'y
dy
+5+6y=3x² +5
dr
dr²
Such that f(0) = 0 and f'(0) = 1
(i) Without solving the differential equation, show that f(0) = -6 and find the value of f(*)(0).
(ii) Hence find the first three non-zero terms in the expansion, in ascending powers of x, of f(x).
(b) Find the general solution of the differential equation
d'y dy
dr² dr
+5- +6y=3x² +5
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