InterviewSolution
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InterviewSolution
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The solution of `(dy)/(dx)=(x^2+y^2+1)/(2x y)`satisfying `y(1)=1`is given by(a) a system of parabolas(b) a system of circles(c)`( d ) (e) (f) y^(( g )2( h ))( i )=x(( j ) (k)1+x (l))-1( m )`(n)(d) `( o ) (p) (q) (r)(( s ) (t) x-2( u ))^(( v )2( w ))( x )+( y ) (z)(( a a ) (bb) y-3( c c ))^(( d d )2( e e ))( f f )=5( g g )`(hh)A. a hyperbolaB. a circleC. `y^(2)=x(1+x)-10`D. `(x-2)^(2)+(y-3)^(2)=5` |
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Answer» Correct Answer - A We have, `(dy)/(dx)=(x^(2)+y^(2)+1)/(2xy)` `rArr" "2xy dy=(x^(2)+y^(2)+1)dx` `rArr" "2xydy-y^(2)dx=(x^(2)+1)dx` `rArr" "xd(y^(2))-y^(2)dx=(x^(2)+1)dx` `rArr" "(xd(y^(2))-y^(2)dx)/(x^(2))=(1+(1)/(x^(2)))dx` `rArr" "d((y^(2))/(x))=d(x-(1)/(x))` On integrating, we get `(y^(2))/(x)=x-(1)/(x)+C` `rArr" "y^(2)=x^(2)-1+Cx rArr y^(2)=(x+(C)/(2))^(2)-1-(C^(2))/(4)` Clearly, it represents a hyperbola. |
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