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53) Which function f(x) = E anx" satisfies the differential equation n=0 f'(x) = -2x f(x)? %3D a) f(x) = Ë(-1)" n=0 b) f(x) = £(-1)" (2n)! n=0 c) f(x) = È(-1)n-1zm=1 n! 22n-1 n=0 00 d) f(x) = E(-1)n-12n+1 n=0 e) None of the above.

53) Which function f(x) = E anx" satisfies the differential equation n=0 f'(x) = -2x f(x)? %3D a) f(x) = Ë(-1)" n=0 b) f(x) = £(-1)" (2n)! n=0 c) f(x) = È(-1)n-1zm=1 n! 22n-1 n=0 00 d) f(x) = E(-1)n-12n+1 n=0 e) None of the above.

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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Solve both 52 and 53 please

f(n) (0) 52) To show that a function f (x) is equal to its Taylor Series x" at some n! n=0 xo E R, fen (0) " converges at xo- a) it suffices to show that п! n=0 00 b) it suffices to show that f"(0), n! converges absolutely at xo. n=0 c) it suffices to show that lim Rn.o(xo) 0. n-00 flr) (0) d) f(x) is always equal to > x" for all x E R. п! n=0 e) None of the above.
Transcribed Image Text:f(n) (0) 52) To show that a function f (x) is equal to its Taylor Series x" at some n! n=0 xo E R, fen (0) " converges at xo- a) it suffices to show that п! n=0 00 b) it suffices to show that f"(0), n! converges absolutely at xo. n=0 c) it suffices to show that lim Rn.o(xo) 0. n-00 flr) (0) d) f(x) is always equal to > x" for all x E R. п! n=0 e) None of the above.
53) Which function f(x) = E anx" satisfies the differential equation n=0 f'(x) = -2x f (x)? a) f(x) = E(-1)" n! n=0 b) f(x) = E(-1)" (2n)! n=0 c) f(x) = E(-1)n-12n=1 n! n=0 .2n+1 d) f(x) = Ë(-1)"-1=*1 n! n=0 e) None of the above.
Transcribed Image Text:53) Which function f(x) = E anx" satisfies the differential equation n=0 f'(x) = -2x f (x)? a) f(x) = E(-1)" n! n=0 b) f(x) = E(-1)" (2n)! n=0 c) f(x) = E(-1)n-12n=1 n! n=0 .2n+1 d) f(x) = Ë(-1)"-1=*1 n! n=0 e) None of the above.
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