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1. Solve the homogeneous Cauchy-Euler initial-value problem: where , , . 2. Solve the homogeneous Cauchy-Euler differential equation: where . 3. Solve the nonhomogeneous Cauchy-Euler differential equation: where . 4. Given the power series expansion: use -substitution to combine the series in terms of . 5. Find the first six nonzero terms for the power series solution to the differential equation: . where . 6. Find the first six nonzero terms for the power series solution to the initial-value problem: where , , . 7. Find the first five nonzero terms for the power series solution to the differential equation:

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