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Question : 111 of 150
Marks:
+1,
-0
Solution:
‌x‌=y+x‌tan‌‌⇒‌‌‌=‌It is a homogeneous differential equation.
Put
y=vx⇒‌‌=v+x‌⇒‌v+x‌‌=‌⇒x‌‌=v+tan‌v−v⇒‌x‌‌=tan‌v⇒‌tan‌v‌=‌⇒cot‌v‌d‌v‌=‌On integrating both sides, we get
‌log‌s‌i‌n‌v‌=log‌x+log‌C⇒‌log‌s‌i‌n‌v‌=log‌x‌C⇒sin‌v‌=xC∴‌sin‌‌‌=Cx‌‌(∵‌ Put ‌v=‌)
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