Problem #1: For which of the cases below do the given functions form a fundamental set of solutions of the correspondingdifferential equation on the indicated interval?(1) y" - 19y+90y = 0; 10e2x, 10e10x, (-∞0,00)(ii) y"-6y +9y = 0; 9e²r, 2re²r, (-00,00)(iii) x²y" - 16xy' + 72y = 0; 9x², 3x¹0, (0, 0)(iv) y" - 10y" - 63y + 648y = 0, ex, xe³x, e-8x, (-∞0, ∞0).(A) (i) and (ii) only (B) (i) and (iv) only(F) (i), (ii), and (iv) only (G) all of them(C) (iii) only (D) (ii) and (iv) only (E) (i) only(H) none of them (I) (iv) only (J) (ii) only(K) (ii), (iii), and (iv) only (L) (i), (iii), and (iv) only (M) (1) and (iii) only (N) (1), (ii), and (iii) only(O) (iii) and (iv) only (P) (ii) and (iii) only

Answered: Image /qna-images/answer/60f2c4b0-c33b-4312-be44-44248947acda.jpg

Problem #1: For which of the cases below do the given functions form a fundamental set of solutions of the corresponding differential equation on the indicated interval? (1) "19y' +90y = 0; 10e2x, 10e10x, (-∞0,00) (ii) y"-6y +9y = 0; 9e²r, 2re2r, (-∞0,00) (iii) x2y"-16xy' + 72y = 0; 9x9, 3x¹0, (0, 0) (iv) y" - 10y" - 63y + 648y = 0, ex, xe³x, e-8x, (-∞0, ∞0). (A) (i) and (ii) only (B) (i) and (iv) only (F) (i), (ii), and (iv) only (G) all of them (C) (iii) only (D) (ii) and (iv) only (E) (i) only (H) none of them (I) (iv) only (J) (ii) only (K) (ii), (iii), and (iv) only (L) (i), (iii), and (iv) only (M) (1) and (iii) only (N) (i), (ii), and (iii) only (O) (iii) and (iv) only (P) (ii) and (iii) only