Question

Choose the appropriate table for the differential equation dy dx equals x divided by y.

x −2 0 1
y −4 1 2
dy dx one half undefined one half


x −2 0 1
y −4 1 2
dy dx one half 0 one half


x −2 0 1
y −4 1 2
dy dx negative one half 0 one half
Cannot be found without solving the differential equation

Answer 1

Explanation:

Given that a differential equation of I order and degree is of the form

`(dy)/(dx)=(x)/(y)`

Cross multiply to separate variables as

ydy = xdx

Integrate both sides to get

`(y^2)/(2) =(x^2)/(2) +C\\x^2-y^2 =C'`

From the options given we find that correct one is

Cannot be found without solving the differential equation

Answer 2

x −2 0 1

y −4 1 2

dy/dx one half 0 one half

Explanation:

Actually, it can be solved without solving the differential equation. You just put the given numbers into the given equation.

dy/dx = x/y

For (x, y) = (-2, -4), dy/dx = (-2)/(-4) = 1/2

For (x, y) = (0, 1), dy/dx = 0/1 = 0

For (x, y) = (1, 2), dy/dx = 1/2