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Question Number 108319 by bobhans last updated on 16/Aug/20
$$\:{find}\:{general}\:{solution}\: \\ $$$$\:\:\:\:\:\:{x}\:\frac{{dy}}{{dx}}\:+\:\mathrm{3}{xy}\:=\:\mathrm{6} \\ $$
Answered by Dwaipayan Shikari last updated on 16/Aug/20
$$\frac{{dy}}{{dx}}+\mathrm{3}{y}=\frac{\mathrm{6}}{{x}} \\ $$$${I}.\:{F}={e}^{\int\mathrm{3}} ={e}^{\mathrm{3}{x}} \\ $$$${y}.{e}^{\mathrm{3}{x}} =\int{e}^{\mathrm{3}{x}} .\frac{\mathrm{6}}{{x}} \\ $$$${y}={Ce}^{−\mathrm{3}{x}} +\mathrm{6}{e}^{−\mathrm{3}{x}} {Ei}\left(\mathrm{3}{x}\right) \\ $$