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Question : 80 of 160
Marks:
+1,
-0
Solution:
‌y=Aex+Bsin‌x‌‌‌⋅⋅⋅⋅⋅⋅⋅(i)‌‌=Aex+B‌cos‌x‌‌‌⋅⋅⋅⋅⋅⋅⋅(ii)‌‌=Aex−Bsin‌x‌‌‌⋅⋅⋅⋅⋅⋅⋅(iii)From Eqs. (i) and (iii),
‌(y+‌)=AexFrom Eqs. (i) and (ii),
B=(y−‌)‌∴ From Eq. (iii),
‌⇒‌‌‌=‌(y+‌)−(y−‌)‌‌⇒‌‌=‌−‌(y−‌)‌⇒(sin‌x−cos‌x)‌=(sin‌x−cos‌x)y‌‌‌−2sin‌x⋅y+2sin‌x‌‌⇒(sin‌x−cos‌x)‌−2sin‌x‌+(2sin‌x−sin‌x+cos‌x)y=0‌⇒(sin‌x−cos‌x)‌−2sin‌x‌+(sin‌x+cos‌x)y=0‌‌‌∴f(x)+g(x)+h(x)‌=sin‌x−cos‌x−2sin‌x+sin‌x+cos‌x‌=0
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