engineering recuitment GATE ECE 2023-24 Test Series Engineering Mathematics Differential Equations Method of Variation of Parameters
Find the particular solution of the differential equation \(\frac{{{{\rm{d}}^2}{\rm{y}}}}{{{\rm{d}}{{\rm{x}}^2}}} - \frac{{4{\rm{dy}}}}{{{\rm{dx}}}} + 4{\rm{y}} = \frac{{{{\rm{e}}^{2{\rm{x}}}}}}{{{{\rm{x}}^2}}}\)
1
\(- {\rm{x}}{{\rm{e}}^{2{\rm{x}}}} - \frac{1}{{\rm{x}}}{\rm{logx}}.{{\rm{e}}^{2{\rm{x}}}}\)
2
\({\rm{x}}{{\rm{e}}^{2{\rm{x}}}} + \frac{1}{{\rm{x}}}{\rm{logx}}{{\rm{e}}^{2{\rm{x}}}}\)
3
\(- {\rm{logx}}.{{\rm{e}}^{2{\rm{x}}}} - \frac{1}{{\rm{x}}}.{{\rm{e}}^{2{\rm{x}}}}\)
4
\(- {{\rm{e}}^{2{\rm{x}}}}\left[ {1 + {\rm{logx}}} \right]\)