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Find the solution of the given initial value problem 52y" + 17y"+y = 0, y(0) = −13, y'(0) = 18, y"(0) = 0. On paper, sketch the graph of the solution. How does the solution behave as t → ∞? y(t) = = As t → ∞, y(t)

Find the general solution of the differential equation. y (5) 7y(4) +11y"" - 7y" +10y' = 0. NOTE: Use C1, C2, C3, C4, and c5 for the arbitrary constants. - 2x y(t) = ₁ + c₂e²x + c3e5x + c₁cos(x) + csin(x) X

Determine the general solution of the given differential equation. y" - y" - y + y = 7e-¹ +5 NOTE: Use C₁, C2, and c3 as arbitrary constants. y(t) =