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MathSofiya

  • 2 years ago

solve the differential equation using the variation of parameters method \[y''+y=sec^2x,0\le x\le \frac{\pi}2\] \[r^2+1=0\]

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  1. Algebraic!
    • 2 years ago
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    did you get that problem from the other day sorted out?

  2. Algebraic!
    • 2 years ago
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    y" +y =t*e^t iirc?

  3. MathSofiya
    • 2 years ago
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    at first I had r^2+r=0 and that gave me the integral of \[\int\frac{e^{-x}sec^2x}{e^{-x}}dx+e^{-x}\int \frac{sec^2x}{e^{-x}}dx\]

  4. MathSofiya
    • 2 years ago
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    but that is apparently wrong

  5. MathSofiya
    • 2 years ago
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    iirc? what does that mean?

  6. Algebraic!
    • 2 years ago
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    if I recall correctly

  7. MathSofiya
    • 2 years ago
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    \[r_1=r_2=\pm1i\]

  8. MathSofiya
    • 2 years ago
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    \[y_c=c_1cosx+c_2sinx\]

  9. MathSofiya
    • 2 years ago
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    \[W(y_1,y_2)=cos^2x+sin^2x\]

  10. Algebraic!
    • 2 years ago
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    1

  11. MathSofiya
    • 2 years ago
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    nice! \[y_p=-cosx\int sinxsec^2xdx+sinx \int cosxsec^2xdx\]

  12. MathSofiya
    • 2 years ago
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    so far so good?

  13. Algebraic!
    • 2 years ago
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    yes

  14. MathSofiya
    • 2 years ago
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    \[y=y_c+y_p=c_1cosx+c_2sinx-cosxsecx+\int cosxsec^2xdx\]

  15. Algebraic!
    • 2 years ago
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    missing a 'sin' on that last term...

  16. psi9epsilon
    • 2 years ago
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    @mathsofiya , check integration seems incomplete

  17. Algebraic!
    • 2 years ago
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    lol

  18. psi9epsilon
    • 2 years ago
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    @Algebraic! , didnt really see the reason for "lol", there are couple of things missing here

  19. Algebraic!
    • 2 years ago
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    "integration seems incomplete"

  20. Algebraic!
    • 2 years ago
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    what tipped you off?

  21. Algebraic!
    • 2 years ago
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    here I thought you were making a funny and you were somehow serious...

  22. psi9epsilon
    • 2 years ago
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    a simple look suggests that last term carries an Integration sign whereas the second last term does not, it cant be both , either we have an integral sign or we dont. Anyways its better to teach something correctly : )

  23. MathSofiya
    • 2 years ago
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    where's a sine missing?

  24. Algebraic!
    • 2 years ago
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    sinx∫cosxsec^2x dx -> ∫cosxsec^2x dx

  25. MathSofiya
    • 2 years ago
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    very true \[y=y_c+y_p=c_1cosx+c_2sinx-cosxsecx+sinx\int cosxsec^2xdx\]

  26. MathSofiya
    • 2 years ago
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    is this really the solution to the integral? http://www.wolframalpha.com/input/?i=integral+of+cosxsec^2x

  27. Algebraic!
    • 2 years ago
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    most people use ln(tan(x) +sec(x)) for brevity

  28. Algebraic!
    • 2 years ago
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    programs always give the other form of the answer; not sure why, probably to confound students.

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