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anonymous

  • 4 years ago

Calculus Help: Show that ln(y)=arctan(x) is a solution to the differential equation (1+x^2)y"+(2x-1)y'=0 I'm totally lost need help!

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  1. mathmate
    • 4 years ago
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    From ln(y)=arcxtan(x), raise to power of e e^(ln(y))=e^(arctan(x)) y=e^arctan(x) now differentiate y to get y', and differentiate twice to get y". Substitute in the given equation's LHS to show that after simplification, the LHS = 0 (for any value of x).

  2. mathmate
    • 4 years ago
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    Hint: you will need the chain rule to do the differentiations.

  3. anonymous
    • 4 years ago
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    Thank you so much mathmate! you're a lifesaver :)

  4. mathmate
    • 4 years ago
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    You're welcome! :)

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