Question

\( \mathrm{EX3} \) ????????????????? \[ \ddot{y}+2 \dot{y}+0.75 y=2 \cos t-0.25 \sin t+0.09 t, \quad y(0)=2.78, \quad y^{\prime}(0)=-0.43 \]

          \( \mathrm{EX3} \) ?????????????????
\[
\ddot{y}+2 \dot{y}+0.75 y=2 \cos t-0.25 \sin t+0.09 t, \quad y(0)=2.78, \quad y^{\prime}(0)=-0.43
\]

EX3 ?????????????????

ÿ+2 ẏ+0.75 y=2 cos t-0.25 sin t+0.09 t, y(0)=2.78, y^'(0)=-0.43

Added by Joseph W.

Fundamentals of Differential Equations

R. Kent Nagle 9th Edition

Chapter 7

Instant Answer

Solved by Expert Tanishq Gupta

07/01/2020

Step 1

Substituting this into the differential equation, we get: \[\ddot{y}_c + 2\dot{y}_c + 0.75y_c = 0\] Differentiating \(y_c(t)\) twice, we get: \[r^2e^{rt} + 2re^{rt} + 0.75e^{rt} = 0\] Factoring out \(e^{rt}\), we get: \[e^{rt}(r^2 + 2r + 0.75) = 0\] Since Show more…

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