We consider the initial value problem 9z?y" + 33zy' + 20y = 0, y(1) = 3, y'(1) - -6 By looking for solutions in the formy - z' in an Euler-Cauchy problem Ar'y" + Bry' + Cy = 0, we obtain a auxiliary equation Ar + (B – A)r +C = 0 which is the analog of the auxiliary equation in the constant coefficient case. (1) For this problem find the auxiliary equation: -0 (2) Find the roots of the auxiliary equation: (enter your results as a comma separated list) (3) Find a fundamental set of solutions y, (enter your results as a comma separated list) (4) Recall that the complementary solution (i.e., the general solution) is ye = ciy1 + c2y2. Find the unique solution satisfying y(1) = 3, y(1) = -6

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A: Since y1 and y2 are two solutions of the non-homogeneous equation, we have y1''+ay1'+by1=c…

Q: 6. Solve the following Euler's equations: (a) x²y" +5xy' + 4y = 0 (b) x²y" - xy + 3y = 0

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