A) \[\sin y-{{e}^{x}}(x-1){{x}^{-4}}\]
B) \[\sin y-{{e}^{x}}(x-1){{x}^{-3}}\]
C) \[\tan y-{{e}^{x}}(x-1){{x}^{-3}}\]
D) \[\tan y-{{e}^{x}}(x-2)logx\]
Correct Answer: A
Solution :
| Given equation can be written as |
| \[{{x}^{4}}\cos y\frac{dy}{dx}+4{{x}^{3}}\sin y=x{{e}^{x}}\]\[\Rightarrow \frac{d}{dx}({{x}^{4}}\sin y)=x{{e}^{x}}\]\[\Rightarrow {{x}^{4}}\sin y=\int{x{{e}^{x}}\,\,\,dx}\]\[\Rightarrow {{x}^{4}}\sin y=(x-1){{e}^{x}}+c\] |
| But when\[x=1,y=0\,\,so\,\,c=0\], Hence required solution is \[\sin y={{x}^{-4}}(x-1){{e}^{x}}\] |
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