(15 points) Find the first three non-zero terms of each of the two linearly inde- pendent...

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(15 points) Find the first three non-zero terms of each of the two linearly inde- pendent series solutions centered at x = 0. 4xy" +3xy+xy = 0. Hint: Assume a solution of the form y(x) = x=0 anx+, and show that 0 = n=0 4(n+r 1)(n+r)anx" + 3(n+r)anx" + an1x. n=0 n=1 Use this to find the indicial equation. Solve for the two values of r. Then use this equation to find the recurrence relation for each r, as we did in class. Finally, use each recurrence relation to find the first three terms for each r. (15 points) Find the first three non-zero terms of each of the two linearly inde- pendent series solutions centered at x = 0. 4xy" +3xy+xy = 0. Hint: Assume a solution of the form y(x) = x=0 anx+, and show that 0 = n=0 4(n+r 1)(n+r)anx" + 3(n+r)anx" + an1x. n=0 n=1 Use this to find the indicial equation. Solve for the two values of r. Then use this equation to find the recurrence relation for each r, as we did in class. Finally, use each recurrence relation to find the first three terms for each r.