A) \[y=ln\,(x)+c\]
B) \[y=\,{{(ln\,x)}^{2}}+c\]
C) \[y=\pm \,ln\,(x)+c\]
D) \[xy={{x}^{y}}+c\]
Correct Answer: C
Solution :
[c] The given equation is reduced to \[x={{e}^{xy(dy/dx)}}\] \[\Rightarrow \ell nx=xy\frac{dy}{dx}\Rightarrow \int{ydy=\int{\frac{1}{x}\ell nxdx}}\] \[\Rightarrow \frac{{{y}^{2}}}{2}=\frac{{{(\ell nx)}^{2}}}{2}+c\] \[\Rightarrow y=\pm \sqrt{{{(\ell nx)}^{2}}}+c=\pm \ell nx+c\]You need to login to perform this action.
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