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

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JenniferSmart1Best ResponseYou've already chosen the best response.1
@hartnn I'm almost done with the question
 one year ago

JenniferSmart1Best ResponseYou've already chosen the best response.1
glad to see you my friend =D
 one year ago

JenniferSmart1Best ResponseYou've already chosen the best response.1
the next step...everything I did so far seems right
 one year ago

JenniferSmart1Best ResponseYou've already chosen the best response.1
ohhh...I plug them back into the original formula!!!
 one year ago

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

JenniferSmart1Best ResponseYou've already chosen the best response.1
and then I....? Yeah that's where I'm stuck :P
 one year ago

JenniferSmart1Best ResponseYou've already chosen the best response.1
what 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?
 one year ago

JenniferSmart1Best ResponseYou've already chosen the best response.1
oh sorry I forgot to write \[y_p'=u_1e^x+u_2e^x+u_2xe^x\]
 one year ago

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

JenniferSmart1Best ResponseYou've already chosen the best response.1
I 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
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.1
you have y_p, y'_p and y''_p insert them into t your original DE and simplify
 one year ago
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