(1) Let Y1 and Y2 be two solution of (i) If W (y₁, y2) is Wronskian of y₁ and y2, show that dW a₂(x). + a₁(x). dx (ii) D

[answerhappygod]

1 Let Y1 And Y2 Be Two Solution Of I If W Y Y2 Is Wronskian Of Y And Y2 Show That Dw A X A X Dx Ii D 1 (89.8 KiB) Viewed 47 times

(1) Let Y1 and Y2 be two solution of (i) If W (y₁, y2) is Wronskian of y₁ and y2, show that dW a₂(x). + a₁(x). dx (ii) Derive Abel's formula a₂(x)y" + a₁(x)y' + ao(x)y= = 0 for xo in I show that where c is a constant. (iii) Using an alternative form of Abel's formula (iv) Show that if W(xo) W0 for every x in the interval. dW dx W = ce-Sla₁(x)/a2(x)] dr = 0. W = ce - [a₁(t)/a₂(t)] dt W(y₁, y2) = W (xo)e¯√x [ª₁(t)/a2(t)] dt = 0, then W = 0 for every x in I whereas if W(x) ‡ 0, then