A) \[y\sin y={{x}^{2}}\log x+\frac{{{x}^{2}}}{y}+c\]
B) \[y\cos y={{x}^{2}}(\log x+1)+c\]
C) \[y\cos y={{x}^{2}}\log x+\frac{{{x}^{2}}}{2}+c\]
D) \[y\sin y={{x}^{2}}\log x+c\]
Correct Answer: D
Solution :
\[(y\cos y+\sin y)dy=(2x\log x+x)dx\] \[y\sin y-\int{\sin y\,\,dy}+\int{\sin y\,\,dy}\] \[={{x}^{2}}\log x-\int{{{x}^{2}}\cdot \frac{1}{x}dx+\int{x\,\,dx+c}}\] \[\therefore \] \[y\sin y={{x}^{2}}\log x+c\]
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