The differential equation of the family of lines passing through the origin is:

Question

The differential equation of the family of lines passing through the origin is: (A)  x(dy/dx)+y=0  (B)  x+(dy/dx)=0  (C)  (dy/dx)=y  (D)  (dy/dx)=x

Tardigrade Admin · Accepted Answer

The equation of line passing through the origin is given by y=mx ...(i) On differentiating w.r.t. x, we get (dy/dx)=m ⇒ (dy/dx)=(y/x) (using Eq. (i)) ⇒ x(dy/dx)-y=0

Q. The differential equation of the family of lines passing through the origin is:

$x \frac{d y}{d x} + y = 0$

$x + \frac{d y}{d x} = 0$

$\frac{d y}{d x} = y$

$\frac{d y}{d x} = x$

$x \frac{d y}{d x} - y = 0$

The equation of line passing through the origin is given by $y = m x$ ...(i) On differentiating w.r.t. $x,$ we get $\frac{d y}{d x} = m$ $\Rightarrow$ $\frac{d y}{d x} = \frac{y}{x}$ (using Eq. (i)) $\Rightarrow$ $x \frac{d y}{d x} - y = 0$

Q. The differential equation of the family of lines passing through the origin is:

xdxdy​+y=0

x+dxdy​=0

dxdy​=y

dxdy​=x

xdxdy​−y=0