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Question : 146 of 150
Marks:
+1,
-0
Solution:
Given, differential equation can be written as
‌=‌or
‌+‌⋅x=‌It is a linear differential equation of the form
‌+Px=Qwhere,
‌‌P=‌and
Q=‌∴ Integrating factor
=e∫Pdy‌=e∫‌dy‌=etan−1y ∴ Solution is
etan−1y⋅x=∫‌dyPut
tan−1y=t in right hand side,
‌⇒‌‌‌dy=dt‌∴‌‌xetan−1y=∫‌‌dt‌=tet−∫1⋅et‌dt+C‌=tet−et+C‌=tan−1y⋅etan−1y−etan−1y+C‌⇒‌‌xetan−1y=(tan−1y−1)etan−1y+C‌
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