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anonymous
 one year ago
Hi fellas! Differential Equation SOS!!!!
anonymous
 one year ago
Hi fellas! Differential Equation SOS!!!!

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[y''+6y'7y=x^2e^x+7e^(7x)+e^(7x)sinx\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I need to write down the general and the private solution of the DE @Loser66

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and THANKS A LOT guys I truly appreciate that!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I know how to get to the general solution, but the private one is killing me

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[yh=C1e ^{7x}+C2e ^{x}+yp\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0can you help me out with the solution of the private solution?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2The homogenious part give you the solutions, right? what are they?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2\(y_h= C_1 e^{7x}+C_2e^x\), right?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2hence \(e^x\) is available. Now private part, the first term is \(x^2e^x\) , that is we have \(y_{p1}= (Ax^2+Bx+C)*x(e^x)\) \(y'_{p1}= you~~ do\) \(y"_{p1} =.....\) then apply to the equation y"+6y'+7y to solve for \(y_{p1}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0not sure I'm following, let me have a look though

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0a couple of minutes I need to sort it out

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2The second term is \(7e^{7x}\) , I do it for you as a sample We need find \(y_{p2}= Dte^{7x}\\y'_{p2}= 7De^{7x}\\y"_{p2}= 49 De^{7x}\) Now combine \(y"_{p2}+6y'_{p2}7y_{p2}= 49De^{7x} 42De^{7x}+7Dte^{7x}= 7e^{7x}\)

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2from that you have \(7De^{7x}+7Dxe^{7x}= 7e^{7x}\) Make a comparison, you have D =1 hence the solution for that is \(y_{p2}= xe^{7x}\) Sorry for t at the beginning, it is x.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sorry but what does D refer to?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2Do the same with the last term\(e^{x} sinx\)

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2and you apply the ODE from the left to solve for D

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wow thanks a lot @Loser66 !

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but please just for clarification

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2D is a constant, like A, B, C for \(y_{p1}\). I use D to make sure that you are not confused and differentiate them.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2when finding private solution for \(e^x sinx\), you need use E, F, G.... to know that those constants are not the constants from \(y_{p1}~~or~~y_{p2}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I hope I'll nail this now
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