P2 Consider the two power series f(x) = x + Σ n=0 g(x) = Σ n=2 (b) Show that f(x) satisfies the equation (3x)2n+1 (2n + 1)! (x + 1)" 3 n ln(n) y" = 9(y-x).

Q: X Find a power series expansion for g(x) = | f(t) dt given the expansion for f(x). sin 19x f(x) =…

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Q: P2 Consider the two power series f(x) = x + Σ n=0 (3x)2n+1 (2n + 1)! (x + 1)" g(x) = Σ 3″n ln(n)*…

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Q: P2 Consider the two power series (3x)2n+1 f(x) = x + Σ (2n + 1)! n=0 (x + 1)" g(x) = 3n ln(n) n=2…

A: We will show that f(x) satisfies the given equation (y=f(x))

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Q: 3. Obtain series solution of the IVP:  (x+1)y''-(2-x)y' + y=0; y(0)=2, y'(0)=-1

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Q: Consider the two power series f(x) = x + Σ n=0 g(x) = Σ n=2 (b) Show that f(x) satisfies the…

A: We have to show that fx=x+∑n=0∞3x2n+12n+1! satisfies y''=9(y-x)

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Q: Q 3. Find the Taylor series of f at the point c for : (a) f(x) = e", c= 2 (c) f(x) = sin x, c= T (b)…

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