x" + 4x'+ 3x = 30 cos(3t), x(0) = 1, x'(0) = 2 Solve the above IVP and then find x(0.25). Put x(0.25) accurately calculated to the nearest thousandth (3 decimal places). Notation: d²x and x' = dx and x = x(t) dt dt

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[ordinary differential equations; topic] Please solve the following problem Provide a well explained and understandable(readable) Step by step solution solution

x" + 4x' + 3x = 30 cos(3t),
x(0) = 1, x'(0) = 2
Solve the above IVP and then find x(0.25).
Put x(0.25) accurately calculated to the nearest thousandth (3 decimal places).
Notation:
d²x
and x' =
dt?
dx
and x = x(t)
dt
Transcribed Image Text:x" + 4x' + 3x = 30 cos(3t), x(0) = 1, x'(0) = 2 Solve the above IVP and then find x(0.25). Put x(0.25) accurately calculated to the nearest thousandth (3 decimal places). Notation: d²x and x' = dt? dx and x = x(t) dt
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