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 differential equation given is

y dy/dx = x

Separate the variables as

ydy = xdx

Integrate to get

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

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

Since y(1) =0

0 = 1+C\'

Or C\' =-1

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

A hyperbola vertical

Since (0,1) lies on the hyperbola, graph a.