Suppose the solution of the differential equation d y d x = (2+ ) x- y+2 x-2 y-( -4 ) represents a circle passing through origin. Then the radius of this circle is :

Step-by-step solution

aligned & d y d x = (2+ ) x- y+2 x-y(2 + )+4 & x d y-(2 + ) y d y+4 d y=(2+ ) x d x- y d x+2 d x & (x d y+y d x)-(2 + ) y d y+4 d y=(2+ ) x d x+2 d x & x y- (2 + ) y^2 2 +4 y= (2+ ) x^2 2 aligned aligned & =0 for this to be circle & (2+ ) x^2 2 + y^2+2 x-4 y=0 aligned aligned & i.e. 2 x^2+2 y^2+2 x-8 y=0 & x^2+y^2+x-4 y=0 & r d= 1 4 +4 = 17 2 aligned