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

This Question is Closed

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

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

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

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

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

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

misha1227 Group TitleBest ResponseYou've already chosen the best response.0
oo for e^(1/2)..?
 3 years ago

watchmath Group TitleBest 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 \(\ln\).
 3 years ago

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

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