Question

solve the next separable ODE and graph the direction field of all solutions...

Answer 1

Starting with
\[\frac{dy}{dx}=\frac{1-x^2}{y^2}\]
Multiply both sides by y^2
\[y^2\frac{dy}{dx}=1-x^2\]
Multiply both sides by \[y^2dy=(1-x^2)dx\]
Integrate both sides
\[\int\limits y^2dy=\int\limits (1-x)dx\]Find the integral and solve for y.

Answer 2

i have troubles in the direction field \[y = \sqrt(1-x^2+c)\]

Answer 3

the direction field is defined by dy/dx

Answer 4

come up with some values for x and y and plug them into dy/dx to define the slope at the point

Answer 5

with initial conditions?

Answer 6

could you draw it?

Answer 7

i cant seem to do much of anything today ... sites gone wacky

Answer 8

say we want a 10x10 grid such that -5<=x<=5; and same for y

-5 -4 -3 -2 -1 0 1 2 3 4 5
-5 (-5,-5) (-5,-4) (-5,-3) ....
-4 (-4,-5) (-4,-4) (-4,-3) ....
-3 ...
-2
-1
0
1
2
3
4
5

the poitns themselves define the x and y values to plug into dy/dx to determine the slopes with

Answer 9

\[\frac{dy}{dx}=\frac{1-(-5)^2}{(-5)^2}=-24/25\]almost a slope of -1 at the point -5,-5

Answer 10

at x=-1 or 1, the slope = 0

Answer 11

i am studying the method of the Isoclines, anyway thanks