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Question : 103 of 150
Marks:
+1,
-0
Solution:
Given, differential equation is
‌x‌=y−x‌tan(‌)‌⇒‌‌‌=‌−tan(‌) . . . (i)
Put
y=vx⇒‌=v+x‌ in Eq. (i), we get
‌v+x‌=v−tan‌v⇒‌‌x‌=v−tan‌v−v=−tan‌v ⇒‌=−‌⇒‌dv=‌On integrating both sides, we get
‌∫‌dv=−∫‌⇒log(sin‌v)=−log‌x+log‌C⇒log(sin‌v)+log‌x=log‌C⇒log(xsin‌v)=log‌C⇒(∵log‌m+log‌n=log‌m‌n)‌xsin‌v=COn putting
v=‌, we get
xsin‌(‌)=Cwhich is the required solution.
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