The direction field for y dyldx x is given Select the graph

The direction field for y dyldx x is given. Select the graph that represents the approximate solution curve that passes through the point y (1) - 0 Select one tb.

Solution

The direction field given is ydy/dx = x

Separate the variables as ydy = xdx

Integrate to get

x^2/2 +C = y^2/2

Or x^2+C\' = y^2

Since y(1) =0

1+C\' =0 or c\'=-1

Hence curve is x^2-y^2 = 1

A hyperbola and hence graph a is right. (Also graph B)