\(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{d}{n}}}}+{y}={x}\)

\(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{d}{n}}}}+{p}{y}={x}\)

\(\displaystyle{I}.{F}.={e}^{{\int{p}{\left.{d}{x}\right.}}}={e}^{{\int{1}{\left.{d}{x}\right.}}}={e}^{{x}}\)

\(\displaystyle{y}{\left({I}.{F}.\right)}=\int{0}{\left.{d}{x}\right.}+{c}\)

\(\displaystyle{e}^{{n}}{y}={\frac{{{x}^{{2}}}}{{{2}}}}+{c}\)

c=1

\(\displaystyle{y}={\frac{{{x}^{{2}}}}{{{2}}}}{e}^{{-{n}}}+{e}^{{-{x}}}\)

\(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{d}{n}}}}+{p}{y}={x}\)

\(\displaystyle{I}.{F}.={e}^{{\int{p}{\left.{d}{x}\right.}}}={e}^{{\int{1}{\left.{d}{x}\right.}}}={e}^{{x}}\)

\(\displaystyle{y}{\left({I}.{F}.\right)}=\int{0}{\left.{d}{x}\right.}+{c}\)

\(\displaystyle{e}^{{n}}{y}={\frac{{{x}^{{2}}}}{{{2}}}}+{c}\)

c=1

\(\displaystyle{y}={\frac{{{x}^{{2}}}}{{{2}}}}{e}^{{-{n}}}+{e}^{{-{x}}}\)