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ketz
 3 years ago
2((d^2)y/dx^2)+4(dy/dx)+7y=(e^x)cosx
Solve this Second order differential equation in terms of yp and yc. Explain the choice of yp. Please reply as soon as possible. Exam question...It's extremely urgent
ketz
 3 years ago
2((d^2)y/dx^2)+4(dy/dx)+7y=(e^x)cosx Solve this Second order differential equation in terms of yp and yc. Explain the choice of yp. Please reply as soon as possible. Exam question...It's extremely urgent

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zepdrix
 3 years ago
Best ResponseYou've already chosen the best response.0Were you able to find the complimentary solution, \(\large y_c\) ?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[y_p = ke^{x}cosx\] \[dy/dp = ke^{x}cosx ke^{x}sinx\] \[d^2y/dp^2 = 2ke^{x}sinx\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0dy/dx and d^2y/dx^2 obviously lol

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0check if the the auxillary equation is 2D^2 +4D+7=0

ketz
 3 years ago
Best ResponseYou've already chosen the best response.0but how did you choose the yp since none of ex and cosx are found in the yc. Hence, no priority is given to either ex or cosx......????

zepdrix
 3 years ago
Best ResponseYou've already chosen the best response.0Since the righthand side is \(\large e^{x}cos x\), I think our particular solution's form will be a little bit more complicated. Since the right side has a cosine, it's telling us the particular will have the form \(\large A\cos x+B\sin x\) And the e^{x} is telling us it will have \(\large Ce^{x}\) So our y_p will be the product of these, I'll combine constants to save us some trouble. \[\large y_p=e^{x}\left(Acos x+B \sin x\right)\] And then you would take the derivative of y_p and the second derivative, \(\large y'_p=? \qquad \qquad \qquad y''_p=?\) And then use that information to plug into your y's in your equation. It's been a while since I've done this, someone can correct me if I'm wrong. But I `think` that's the y_p form that we're looking for.

zepdrix
 3 years ago
Best ResponseYou've already chosen the best response.0Did your \(\large y_c\) give you this? This is what I'm coming up with, \[\large y_c=c_1e^{x}\cos\left(\frac{\sqrt{10}}{2}x\right)+c_2e^{x}\sin\left(\frac{\sqrt{10}}{2}x\right)\]

zepdrix
 3 years ago
Best ResponseYou've already chosen the best response.0Because the Auxiliary Equation gave me these roots,\[\large \lambda =1\pm\frac{\sqrt{10}}{2}i\]
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