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malevolence19 Group TitleBest 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: \[y_p(t)=Ate^{3t}\]
 one year ago

sirm3d Group TitleBest ResponseYou've already chosen the best response.0
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

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