A) \[y=\log (\sec x)+(x-2){{e}^{x}}+{{c}_{1}}x+{{c}_{2}}\]
B) \[y=\log (\sec x)+(x+2){{e}^{x}}+{{c}_{1}}x+{{c}_{2}}\]
C) \[y=\log (\sec x)-(x+2){{e}^{x}}+{{c}_{1}}x+{{c}_{2}}\]
D) None of these
Correct Answer: A
Solution :
\[\frac{{{d}^{2}}y}{d{{x}^{2}}}={{\sec }^{2}}x+x{{e}^{x}}\] On integrating, \[\frac{dy}{dx}=\tan x+x{{e}^{x}}-{{e}^{x}}+{{c}_{1}}\] Again, \[y=\log (\sec x)+x{{e}^{x}}-{{e}^{x}}-{{e}^{x}}+{{c}_{1}}x+{{c}_{2}}\] Thus required solution is \[y=\log (\sec x)+(x-2){{e}^{x}}+{{c}_{1}}x+{{c}_{2}}\].
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