A) \[\frac{y}{x}+{{e}^{x}}=c\]
B) \[\frac{x}{y}+{{e}^{x}}=c\]
C) \[x+{{e}^{y}}=c\]
D) \[y+{{e}^{x}}=c\]
Correct Answer: A
Solution :
Given equation is \[x\,dy-y\,dx+{{x}^{2}}{{e}^{x}}dx=0\] \[\Rightarrow \] \[x\,dy-y\,dx+{{x}^{2}}{{e}^{x}}dx=0\] \[\Rightarrow \] \[\frac{x\,dy-ydx}{{{x}^{2}}}+{{e}^{x}}dx=0\] \[\Rightarrow \] \[d\left( \frac{y}{x} \right)+d({{e}^{x}})=0\] On integrating both sides, we get \[\frac{y}{x}+{{e}^{x}}=c\]
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