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misha1227

  • 3 years ago

solve this differential equation!?! (x^2 + a^2)y' = xy please help..

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  1. inik
    • 3 years ago
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    dy/y = x/(x^2+a^2) dx integral each side...

  2. watchmath
    • 3 years ago
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    \(\int\frac{dy}{y}=\int\frac{x\,dx}{a^2+x^2}\) \(\ln|y|=\frac{1}{2}\ln(a^2+x^2)+C\)

  3. misha1227
    • 3 years ago
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    oo ok..and we just solve for y?

  4. A7med
    • 3 years ago
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    use e

  5. watchmath
    • 3 years ago
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    \(|y|=Ae^{\ln(\sqrt{a^2+x^2})}=A\sqrt{a^2+x^2}\) \(y=\pm A\sqrt{a^2+x^2}=A\sqrt{a^2+x^2}\)

  6. misha1227
    • 3 years ago
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    what is the capital A??

  7. watchmath
    • 3 years ago
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    That is to replace \(e^C\) which is just another constant.

  8. misha1227
    • 3 years ago
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    oo for e^(1/2)..?

  9. A7med
    • 3 years ago
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    no for e^c

  10. watchmath
    • 3 years ago
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    \(\frac{1}{2}\ln (a^2+x^2)=\ln(a^2+x^2)^{1/2}\) by the property of \(\ln\).

  11. misha1227
    • 3 years ago
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    yes..i understand it now thanks guys!

  12. watchmath
    • 3 years ago
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    I think we need to add small detail that \(A >0\).

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spraguer (Moderator)
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