question_answer

The solution of the differential equation \[\frac{x+\frac{{{x}^{3}}}{3!}+\frac{{{x}^{5}}}{5!}+.......}{1+\frac{{{x}^{2}}}{2!}+\frac{{{x}^{4}}}{4!}+.......}=\frac{dx-dy}{dx+dy}\]  is __________.

A)  \[2y{{e}^{2x}}=C{{e}^{2x}}-1\]

B)  \[2y{{e}^{2x}}=C{{e}^{2x}}+1\]

C)  \[y{{e}^{2x}}=C{{e}^{2x}}+2\]     

D)  \[y{{e}^{2x}}=C{{e}^{2x}}-2\]

E)  None of these