Question

Given the differential equation: $(1+x^2)y'' + 2xy' - 2y = 0$ with $y(0) = -1$, $y'(0) = -1$ and assume a solution of the form $y = \sum_{n=0}^{8} c_n x^n$. Choose all the correct answers below. (A) $y = x$ (B) $y = 1 + x \arctan(x)$ (C) $y = 1 + x + x \arctan(x)$ (D) $y = 2x - 2 - 2x \arctan(x)$ (E) $y = -2 - 2x - 2x \arctan(x)$ (F) $y = -1 - x - x \arctan(x)$ (G) $y = x - 1 - x \arctan(x)$ (H) $y = 2 - 2x + 2x \arctan(x)$ (I) $y = 1 - x + x \arctan(x)$ (J) $y = 2 + 2x + 2x \arctan(x)$

          Given the differential equation:
$(1+x^2)y'' + 2xy' - 2y = 0$ with $y(0) = -1$, $y'(0) = -1$ and assume a solution of the form $y = \sum_{n=0}^{8} c_n x^n$.
Choose all the correct answers below.
(A) $y = x$
(B) $y = 1 + x \arctan(x)$
(C) $y = 1 + x + x \arctan(x)$
(D) $y = 2x - 2 - 2x \arctan(x)$
(E) $y = -2 - 2x - 2x \arctan(x)$
(F) $y = -1 - x - x \arctan(x)$
(G) $y = x - 1 - x \arctan(x)$
(H) $y = 2 - 2x + 2x \arctan(x)$
(I) $y = 1 - x + x \arctan(x)$
(J) $y = 2 + 2x + 2x \arctan(x)$

Given the differential equation:
(1+x^2)y” + 2xy' - 2y = 0 with y(0) = -1, y'(0) = -1 and assume a solution of the form y = ∑n=0^8 cn x^n.
Choose all the correct answers below.
(A) y = x
(B) y = 1 + x arctan(x)
(C) y = 1 + x + x arctan(x)
(D) y = 2x - 2 - 2x arctan(x)
(E) y = -2 - 2x - 2x arctan(x)
(F) y = -1 - x - x arctan(x)
(G) y = x - 1 - x arctan(x)
(H) y = 2 - 2x + 2x arctan(x)
(I) y = 1 - x + x arctan(x)
(J) y = 2 + 2x + 2x arctan(x)

Added by Evan S.

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