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JenniferSmart1

  • 3 years ago

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

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  1. JenniferSmart1
    • 3 years ago
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    @UnkleRhaukus

  2. JenniferSmart1
    • 3 years ago
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    @radar

  3. JenniferSmart1
    • 3 years ago
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    @hartnn I'm almost done with the question

  4. JenniferSmart1
    • 3 years ago
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    glad to see you my friend =D

  5. JenniferSmart1
    • 3 years ago
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    the next step...everything I did so far seems right

  6. JenniferSmart1
    • 3 years ago
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    ohhh...I plug them back into the original formula!!!

  7. hartnn
    • 3 years ago
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    and then compare the co-efficients.

  8. JenniferSmart1
    • 3 years ago
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    and then I....? Yeah that's where I'm stuck :P

  9. JenniferSmart1
    • 3 years ago
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    oh ok

  10. JenniferSmart1
    • 3 years ago
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    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?

  11. JenniferSmart1
    • 3 years ago
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    sry :S

  12. JenniferSmart1
    • 3 years ago
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  13. JenniferSmart1
    • 3 years ago
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    oh sorry I forgot to write \[y_p'=u_1e^x+u_2e^x+u_2xe^x\]

  14. oldrin.bataku
    • 3 years ago
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    Hey, is that the Stewart book?

  15. JenniferSmart1
    • 3 years ago
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    yes

  16. JenniferSmart1
    • 3 years ago
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    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

  17. UnkleRhaukus
    • 3 years ago
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    you have y_p, y'_p and y''_p insert them into t your original DE and simplify

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