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 2 years ago
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Variation of parameters
\[y''2y'+y=e^{2x}\]
\[r^22r+1=0\]
\[(r1)^2=0\]
\[r=1\]
\[y_c(x)=c_1e^x+c_2xe^x\]
\[y_p(x)=u_1e^x+u_2xe^x\]
\[y_p'(x)=u_1'e^x+u_2'xe^x+u_1e^x+u_2e^x+u_2xe^x\]
\[u_1'e^x+u_2'xe^x=0\]
\[y_p'=u_1e^x+u_2e^x+u_2xe^x\]
\[y_p''(x)=u_1e^x+u_1e^x+u_2'e^x+u_2e^x+u_2'xe^x+u_2e^x+u_2xe^x\]
 2 years ago
Who can help me? Variation of parameters \[y''2y'+y=e^{2x}\] \[r^22r+1=0\] \[(r1)^2=0\] \[r=1\] \[y_c(x)=c_1e^x+c_2xe^x\] \[y_p(x)=u_1e^x+u_2xe^x\] \[y_p'(x)=u_1'e^x+u_2'xe^x+u_1e^x+u_2e^x+u_2xe^x\] \[u_1'e^x+u_2'xe^x=0\] \[y_p'=u_1e^x+u_2e^x+u_2xe^x\] \[y_p''(x)=u_1e^x+u_1e^x+u_2'e^x+u_2e^x+u_2'xe^x+u_2e^x+u_2xe^x\]

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JenniferSmart1
 2 years ago
Best ResponseYou've already chosen the best response.1@hartnn I'm almost done with the question

JenniferSmart1
 2 years ago
Best ResponseYou've already chosen the best response.1glad to see you my friend =D

JenniferSmart1
 2 years ago
Best ResponseYou've already chosen the best response.1the next step...everything I did so far seems right

JenniferSmart1
 2 years ago
Best ResponseYou've already chosen the best response.1ohhh...I plug them back into the original formula!!!

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.0and then compare the coefficients.

JenniferSmart1
 2 years ago
Best ResponseYou've already chosen the best response.1and then I....? Yeah that's where I'm stuck :P

JenniferSmart1
 2 years ago
Best ResponseYou've already chosen the best response.1what am I looking for when I compare the coeffients....sorry don't mean to ask dumb questions...but what is my eventual goal? Do I have to manipulate the coeffients if they're diffferent?

JenniferSmart1
 2 years ago
Best ResponseYou've already chosen the best response.1oh sorry I forgot to write \[y_p'=u_1e^x+u_2e^x+u_2xe^x\]

oldrin.bataku
 2 years ago
Best ResponseYou've already chosen the best response.0Hey, is that the Stewart book?

JenniferSmart1
 2 years ago
Best ResponseYou've already chosen the best response.1I solved it using undetermined coefficients and I got \[y=y_c+y_p\] \[y=c_1e^x+c_2xe^x+e^{2x}\] and then I was asked to solve the same problem using variation of parameters

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1you have y_p, y'_p and y''_p insert them into t your original DE and simplify
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