The general solution of the differential equation (d y/d x)=(1-x/y) is a family of curves which looks most like which of the following?

Question

The general solution of the differential equation (d y/d x)=(1-x/y) is a family of curves which looks most like which of the following? (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Note: Family of concentric circles with (1,0) as the centre and variable radius ∫ ydy =∫(1-x) dx (y2/2)=x-(x2/2)+C x2+y2-2 x=C ( x -1)2+ y 2= C +1= C ⇒ (B)

Q. The general solution of the differential equation $\frac{d y}{d x} = \frac{1 - x}{y}$ is a family of curves which looks most like which of the following?

Note: Family of concentric circles with $(1, 0)$ as the centre and variable radius
$\int y d y = \int (1 - x) d x$
$\frac{y ^{2}}{2} = x - \frac{x ^{2}}{2} + C$
$x^{2} + y^{2} - 2 x = C$
$(x - 1)^{2} + y^{2} = C + 1 = C \Rightarrow (B)$

Q. The general solution of the differential equation dxdy​=y1−x​ is a family of curves which looks most like which of the following?

Note: Family of concentric circles with (1,0) as the centre and variable radius ∫ydy=∫(1−x)dx 2y2​=x−2x2​+C x2+y2−2x=C (x−1)2+y2=C+1=C⇒(B)

Q. The general solution of the differential equation $\frac{d y}{d x} = \frac{1 - x}{y}$ is a family of curves which looks most like which of the following?

Note: Family of concentric circles with $(1, 0)$ as the centre and variable radius
$\int y d y = \int (1 - x) d x$
$\frac{y ^{2}}{2} = x - \frac{x ^{2}}{2} + C$
$x^{2} + y^{2} - 2 x = C$
$(x - 1)^{2} + y^{2} = C + 1 = C \Rightarrow (B)$