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For $$\frac{{{{\text{d}}^2}{\text{y}}}}{{{\text{d}}{{\text{x}}^2}}} + 4\frac{{{\text{dy}}}}{{{\text{dx}}}} + 3{\text{y}} = 3{{\text{e}}^{2{\text{x}}}},$$     the particular integral is

For $$\frac{{{{\text{d}}^2}{\text{y}}}}{{{\text{d}}{{\text{x}}^2}}} + 4\frac{{{\text{dy}}}}{{{\text{dx}}}} + 3{\text{y}} = 3{{\text{e}}^{2{\text{x}}}},$$     the particular integral is Correct Answer $$\frac{1}{5}{{\text{e}}^{2{\text{x}}}}$$

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