The complimentary function of differential equation \(\frac{{{{\rm{d}}^{\rm{2}}}{\rm{y}}}}{{{\rm{d}}{{\rm{x}}^{\rm{2}}}}}\,\,{\rm{ + }}\,\,\left( {{\rm{1 - cot}}\,{\rm{x}}} \right)\frac{{{\rm{dy}}}}{{{\rm{dx}}}}\,{\rm{ - }}\,{\rm{y}}\,{\rm{cot}}\,{\rm{x}}\,{\rm{ = }}\,{\rm{si}}{{\rm{n}}^{\rm{2}}}{\rm{x}}\), is:
1
c1ex + c2 (sin x - cos x)
2
c1e-x + \(\frac{1}{2}\) c2 (sin x + cos x)
3
c1e-x + c2 (cos x - sin x)
4
c1ex + \(\frac{1}{2}\)c2 (sin x - cos x)
5
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