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 one year ago
Who can help me?
Variation of parameters
\[y''2y'+y=e^{2x}\]
\[r^22r+1=0\]
\[(r1)^2=0\]
\[r=1\]
\[y_c(x)=c_1e^x+c_2xe^x\]
\[y_p(x)=u_1e^x+u_2xe^x\]
\[y_p'(x)=u_1'e^x+u_2'xe^x+u_1e^x+u_2e^x+u_2xe^x\]
\[u_1'e^x+u_2'xe^x=0\]
\[y_p'=u_1e^x+u_2e^x+u_2xe^x\]
\[y_p''(x)=u_1e^x+u_1e^x+u_2'e^x+u_2e^x+u_2'xe^x+u_2e^x+u_2xe^x\]
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.1@hartnn I'm almost done with the question

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

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

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

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

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

JenniferSmart1
 one year 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
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.0Hey, is that the Stewart book?

JenniferSmart1
 one year 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
 one year 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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