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Question : 79 of 160
Marks:
+1,
-0
Solution:
‌‌=‌⇒y=vx⇒v=‌⇒‌‌‌=v+x‌⇒v+x‌=‌⇒v+x‌=‌⇒x‌=‌−v⇒=‌⇒x‌=‌⇒‌dv=‌‌dxIntegrating both sides, we get
‌⇒‌‌∫‌dv=∫‌‌dx‌⇒‌‌log‌x=∫‌dv−∫‌dv‌⇒‌‌log‌x=tan−1v−‌‌∫‌‌dtwhere,
1+v2=t2vdv=dt‌vdv=‌‌dt‌⇒log‌x=tan−1v−‌‌log‌|1+v2|+C‌⇒log‌x=tan−1‌−‌‌log‌|1+‌|+C‌⇒log‌x=tan−1‌−‌‌log‌|‌|+C‌⇒tan−1(‌)=log(c√x2+y2)
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