misha1227
solve this differential equation!?!
(x^2 + a^2)y' = xy
please help..



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inik
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dy/y = x/(x^2+a^2) dx
integral each side...

watchmath
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\(\int\frac{dy}{y}=\int\frac{x\,dx}{a^2+x^2}\)
\(\lny=\frac{1}{2}\ln(a^2+x^2)+C\)

misha1227
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oo ok..and we just solve for y?

A7med
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use e

watchmath
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\(y=Ae^{\ln(\sqrt{a^2+x^2})}=A\sqrt{a^2+x^2}\)
\(y=\pm A\sqrt{a^2+x^2}=A\sqrt{a^2+x^2}\)

misha1227
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what is the capital A??

watchmath
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That is to replace \(e^C\) which is just another constant.

misha1227
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oo for e^(1/2)..?

A7med
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no
for e^c

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

misha1227
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yes..i understand it now thanks guys!

watchmath
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I think we need to add small detail that \(A >0\).