What does the solution of the following ordinary differential equation represent?a)A parabolab)A circlec)An ellipsed)A hyperbolaCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Y.dy/dx+x=o

the above equation can be written as follows

y.y'+X=0 which is a simple 1st order linear equation

which can be solved using variable separable method,

y.y'= -x
y.dy/dx= -x
y.dy =-x.dx
integrating on both sides
we get,y^2/2=-x^2/2
y^2+x^2=o
we know general form of circle is x^2+y^2=r^2
hence on comparison we can note that it is a point circle

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