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

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inik
 3 years ago
Best ResponseYou've already chosen the best response.0dy/y = x/(x^2+a^2) dx integral each side...

watchmath
 3 years ago
Best ResponseYou've already chosen the best response.1\(\int\frac{dy}{y}=\int\frac{x\,dx}{a^2+x^2}\) \(\lny=\frac{1}{2}\ln(a^2+x^2)+C\)

misha1227
 3 years ago
Best ResponseYou've already chosen the best response.0oo ok..and we just solve for y?

watchmath
 3 years ago
Best ResponseYou've already chosen the best response.1\(y=Ae^{\ln(\sqrt{a^2+x^2})}=A\sqrt{a^2+x^2}\) \(y=\pm A\sqrt{a^2+x^2}=A\sqrt{a^2+x^2}\)

misha1227
 3 years ago
Best ResponseYou've already chosen the best response.0what is the capital A??

watchmath
 3 years ago
Best ResponseYou've already chosen the best response.1That is to replace \(e^C\) which is just another constant.

watchmath
 3 years ago
Best ResponseYou've already chosen the best response.1\(\frac{1}{2}\ln (a^2+x^2)=\ln(a^2+x^2)^{1/2}\) by the property of \(\ln\).

misha1227
 3 years ago
Best ResponseYou've already chosen the best response.0yes..i understand it now thanks guys!

watchmath
 3 years ago
Best ResponseYou've already chosen the best response.1I think we need to add small detail that \(A >0\).
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