(1) Let Y1 and 3/2 be two solution of (2) If W (31, 32) is Wronskian of y₁ and 32, show that dW dW a₂(x)- + a₁(x)- = 0.

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1 Let Y1 And 3 2 Be Two Solution Of 2 If W 31 32 Is Wronskian Of Y And 32 Show That Dw Dw A X A X 0 1 (28.75 KiB) Viewed 9 times

(1) Let Y1 and 3/2 be two solution of (2) If W (31, 32) is Wronskian of y₁ and 32, show that dW dW a₂(x)- + a₁(x)- = 0. dx dax (ii) Derive Abel's formula a₂(x)y" + a₁(x)y' + ao(x)y=0 for xo in I show that I W = ce-Sla1(x)/02 (2)] dz where c is a constant. (iii) Using an alternative form of Abel's formula -Slax (t)/a2(t)] W = ce dt W(31,32) = W (ro)elax (t)/a₂(t)) dt (iv) Show that if W(zo) = 0, then W = 0 for every x in I whereas if W(zo) # 0, then W #0 for every x in the interval.