A) \[{{e}^{t}}(\cos t+\sin t)\]
B) \[{{e}^{t}}(\cos t-\sin t)\]
C) \[2{{e}^{t}}(\cos t-\sin t)\]
D) \[2{{e}^{t}}(\cos t+\sin t)\]
E) \[{{e}^{2t}}(\sin t-\cos t)\]
Correct Answer: D
Solution :
\[s={{e}^{t}}(\sin t-\cos t)\] \[\frac{ds}{dt}={{e}^{t}}(\cos t+\sin t)+{{e}^{t}}(\sin t-\cos t)\] \[\frac{ds}{dt}={{e}^{t}}(2\sin t)\] \[\frac{{{d}^{2}}s}{d{{t}^{2}}}=2{{e}^{t}}\cos t+2\sin t\,{{e}^{t}}=2{{e}^{t}}(\cos t+\sin t)\]
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