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Question : 130 of 160
Marks:
+1,
-0
Solution:
We have,
‌y2‌dx+(x2−xy+y2)dy=0⇒‌‌‌=‌It is a homogeneous linear differential equation
‌‌ Put ‌y=vx⇒‌=v+x‌‌∴‌‌v+x‌=‌=‌‌‌‌‌‌‌‌x‌=‌| −v2−v3+v2−v |
| v2−v+1 |
=‌‌⇒‌‌‌dv=‌‌dx‌⇒‌‌‌dv=‌‌dx‌∴‌‌−‌dv+‌dv=‌‌dx On integrating both sides, we get
⇒−log‌v+tan−1v‌=log‌x+C⇒tan−1v‌=log‌x‌v+C‌∴‌tan−1(‌)‌=log‌y+C
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