A) \[{{y}^{2}}(\log \,y)-{{e}^{x}}{{\sin }^{2}}x+c=0\]
B) \[{{y}^{2}}(\log \,y)-{{e}^{x}}{{\cos }^{2}}x+c=0\]
C) \[{{y}^{2}}(\log \,y)+{{e}^{x}}{{\cos }^{2}}x+c=0\]
D) None of these
Correct Answer: A
Solution :
[a] \[\frac{dy}{dx}=\frac{{{e}^{x}}(si{{n}^{2}}x+sin2x)}{y(2logy+1)}\] \[\Rightarrow \int{(2ylogy+y)dy=\int{{{e}^{x}}(si{{n}^{2}}x+sin2x)dx}}\] On integrating by parts, we get \[{{y}^{2}}(logy)={{e}^{x}}{{\sin }^{2}}x+c.\]
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