A) \[(y+3)={{x}^{2}}\]
B) \[{{x}^{2}}(y+3)=1\]
C) \[{{x}^{4}}(y+3)=1\]
D) \[{{x}^{2}}{{(y+3)}^{3}}={{e}^{y+2}}\]
E) \[{{x}^{2}}{{(y+3)}^{2}}={{e}^{y+2}}\]
Correct Answer: D
Solution :
Given that, \[2(y+3)-xy\frac{dy}{dx}=0\] \[\Rightarrow \] \[2(y+3)=xy\frac{dy}{dx}\] On integrating, we get \[\int{\frac{2}{x}}dx=\int{\frac{y}{y+3}}dy\] \[\Rightarrow \] \[2\log x=y-3\log (y+3)+c\] Put\[x=1\]and\[y=-2\]. \[\Rightarrow \] \[2=c\] \[\therefore \] \[{{x}^{2}}{{(y+3)}^{3}}={{e}^{y+2}}\]
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