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Kaydian Group Title

3d2y/dt2-dy/dt +2y=e-3t Differential Equation

  • one year ago
  • one year ago

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  1. malevolence19 Group Title
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    \[\frac{d^2 y}{dt^2}-\frac{1}{3} \frac{dy}{dt}+\frac{2 y}{3}=\frac{e^{-3t}}{3}\] Solve the homogenous part (=0). Then try a solution of the form: \[y_p(t)=Ae^{-3t}\] And differentiate and plug in. Be careful that your homogenous solution doesn't have a root of 3 or else you need something like: \[y_p(t)=Ate^{-3t}\]

    • one year ago
  2. sirm3d Group Title
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    the characteristic root of the homogeneous DE are complex numbers, different from the characteristic root of the RHS. writing the LHS as \(f(D)y\) you can determine right away the particular solution \[y_p=\frac{e^{-3t}}{f(-3)}\]

    • one year ago
  3. sirm3d Group Title
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    minor correction:\[\Huge y_p=\frac{\frac{e^{-3t}}{3}}{f(-3)}\]

    • one year ago
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