b) Determine the general solution of the inhomogeneous linear differential equation y′ = [xy / (1+x^2)] + SQRT [ (1+x^2) / (1-x^2)] by the method of integrating factor.
Last edited by rajr; February 1st 2009 at 11:13 AM.
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Originally Posted by rajr b) Determine the general solution of the inhomogeneous linear differential equation y′ = [xy / (1+x^2)] + SQRT [ (1+x^2) / (1-x^2)] by the method of integrating factor. First, rewrite the DE as follows: The integrating factor would be By u-substitution, it can be shown that Thus, the DE becomes It should be pretty straightforward from here. Does this make sense?
hi thx for ur help should i then integrate both sides to get Y
no you just integrate the left side and you should be left with an answer like y=(1+x^2)^-1/2[sin^-1(x)+C]
thx for ur help
Last edited by rajr; February 1st 2009 at 12:00 PM.
Originally Posted by anon18 no you just integrate the left side and you should be left with an answer like y=(1+x^2)^-1/2[sin^-1(x)+C] No. You integrate both sides to get . When writing the solution, though, we usually prefer to write it as
thx for ur help Mr Chris....
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