Verify that the indicated family of functions is a solution of the given differential equation. Assume an appropriate interval I of definition for each solution. d²y dx² When y = c₁e4x + ₂xe¹x, dy = dx d²y dx² gdy + 16y=0; y = c₁₂e4x + ₁ dx = Thus, in terms of x, d²y dy - 8 + 16y = dx² dx = C₂xe4x + 16(c₁e4x + C₂xe4x)

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