dx dx +8. + 16x = (for t> 0). di dt 1+2

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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**Differential Equation Problem:**

Find the general solution to the differential equation:

\[
\frac{d^2x}{dt^2} + 8 \frac{dx}{dt} + 16x = \frac{e^{-4t}}{1 + t^2} \quad \text{(for } t > 0\text{)}.
\] 

This problem involves solving a second-order linear differential equation with constant coefficients and a non-homogeneous term on the right-hand side. The solution requires finding both the complementary (homogeneous) solution and a particular solution.
Transcribed Image Text:**Differential Equation Problem:** Find the general solution to the differential equation: \[ \frac{d^2x}{dt^2} + 8 \frac{dx}{dt} + 16x = \frac{e^{-4t}}{1 + t^2} \quad \text{(for } t > 0\text{)}. \] This problem involves solving a second-order linear differential equation with constant coefficients and a non-homogeneous term on the right-hand side. The solution requires finding both the complementary (homogeneous) solution and a particular solution.
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