A) \[x\]
B) \[2x\]
C) \[{{e}^{x\log x}}\]
D) \[{{e}^{x}}\]
E) \[x{{e}^{x}}\]
Correct Answer: E
Solution :
Given differential equation is \[x\frac{dy}{dx}+(1+x)y=x\] \[\Rightarrow \] \[\frac{dy}{dx}+\left( \frac{1+x}{x} \right)y=1\] Which is linear differential equation Hence, \[IF={{e}^{\int{\frac{1+x}{x}dx}}}={{e}^{\int{\left( \frac{1}{x}+1 \right)}dx}}\] \[={{e}^{\log x+x}}\] \[={{e}^{\log x}}.{{e}^{x}}\] \[=x{{e}^{x}}\]
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