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Determinetthetsolutionstfortthetfollowingtproblems i) Euler-CauchytEquation: x2 d2y dy + ax + by = c, where a = 4, b = 6, c = 10 2 dx dx

Determine\tthe\tsolutions\tfor\tthe\tfollowing\tproblems i) Euler-Cauchy\tEquation: x2 d2y dy + ax + by = c, where a = 4, b = 6, c = 10 2 dx dx ii) Initial\tvalue\tproblem\tfor\ta\tlinear\tODE\twith\tconstant\tcoefficients: d2y dy x dy + 2 + 2y = e x/2 sin ; y x=0 = 0 =1 2 dx dx 2 dx x=0

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