A) \[(a+m)\,y={{e}^{mx}}+c\]
B) \[y{{e}^{ax}}=m{{e}^{mx}}+c\]
C) \[y={{e}^{mx}}+c{{e}^{-ax}}\]
D) \[(a+m)y={{e}^{mx}}+c{{e}^{-ax}}(a+m)\]
Correct Answer: D
Solution :
I.F. \[={{e}^{\int_{{}}^{{}}{a\,dx}}}={{e}^{ax}}\] \[\therefore \]Required solution is given by \[y.\,{{e}^{ax}}=\int_{{}}^{{}}{{{e}^{mx}}.{{e}^{ax}}}dx=\frac{{{e}^{(a+m)x}}}{a+m}+C\] Þ \[y=\frac{{{e}^{mx}}}{a+m}+C{{e}^{-ax}}\] Þ \[y(a+m)={{e}^{mx}}+C(a+m)\text{ }{{e}^{-ax}}\].
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