Question
The general solution of y2 dx+(x2−xy+y2)dy=0 is
[EAMCET 2003]
[EAMCET 2003]
Answer: Option A
:
A
dxdy+x2−xy+y2y2=0dxdy+(xy)2−(xy)+1=0
Put v=x/y⇒x=vy⇒dxdy=v+ydvdyv+ydvdy+v2−v+1=0⇒dvv2+1+dyy=0⇒∫dvv2+1+∫dyy=0⇒tan−1(v)+logy+C=0⇒tan−1(x/y)+logy+c=0.
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:
A
dxdy+x2−xy+y2y2=0dxdy+(xy)2−(xy)+1=0
Put v=x/y⇒x=vy⇒dxdy=v+ydvdyv+ydvdy+v2−v+1=0⇒dvv2+1+dyy=0⇒∫dvv2+1+∫dyy=0⇒tan−1(v)+logy+C=0⇒tan−1(x/y)+logy+c=0.
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