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Kaydian
 2 years ago
3d2y/dt2dy/dt +2y=e3t Differential Equation
Kaydian
 2 years ago
3d2y/dt2dy/dt +2y=e3t Differential Equation

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malevolence19
 2 years ago
Best ResponseYou've already chosen the best response.0\[\frac{d^2 y}{dt^2}\frac{1}{3} \frac{dy}{dt}+\frac{2 y}{3}=\frac{e^{3t}}{3}\] 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: \[y_p(t)=Ate^{3t}\]

sirm3d
 2 years ago
Best ResponseYou've already chosen the best response.0the 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 \[y_p=\frac{e^{3t}}{f(3)}\]

sirm3d
 2 years ago
Best ResponseYou've already chosen the best response.0minor correction:\[\Huge y_p=\frac{\frac{e^{3t}}{3}}{f(3)}\]
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