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# Answer the following question.. 1. On (-1, 1), two functions y1 (x)...

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3. On (-oo, co), three functions y1 (x) = cos 2x, y2(x) = sin x, y3(x) = cos' r are 1 point linearly independent linearly dependent

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4. Given that y1 = e&quot; is a solution of xy&quot; + (1 -2x)y' + (x -1)y = 0, find its second solution yz on (0, oo), which 1 point is linearly independent from y1. O(x-1)et e -2 Inc e : Inc

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5. Find the value (Ml) for a solution ﬁx) to the initial value problem: 1|...th [1 + 2m]y" + 43:3,&quot; — 4y 2 U; 9(0) 2 1,3,-'(l1l}I = —1 —2:: given that e is a solution to (1 + 2.1:)y" + 4my' — 43; = 0. tie-2 an E] 6—21.112 |:| 1+3&quot;2

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