The general solution of ordinary differential equation (X-9) dy / DX = (6y-3) ^ 2

The general solution of ordinary differential equation (X-9) dy / DX = (6y-3) ^ 2

Separation of variables method
dy/(6y-3)^2=dx/(x-9)
-d(6y-3)/(6y-3)^2=-6dx(x-9)
Integral: 1 / (6y-3) = - 6ln | X-9 | + C1

From the equation system x ^ 2 + y ^ 2-xy + 3x = 1y is the implicit function of X, find dy

2xdx＋2ydy-ydx-xdy＋3dx=0
（2y-x）dy=-（2x-y＋3）dx
dy=-（2x-y＋3）/（2y-x）dx

Calculate ∫ (4x-6) / (x ^ 2-3x + 9) DX,

(4x-6) / (x \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\it's not easy

In the space rectangular coordinate system, if a (1,2, - 1), B (0, - 1,3) are known, does anyone know the distance between two points AB?

The distance between two points of AB is [(x1-x2) ^ 2 + (y1-y2) ^ 2 + (z1-z2) ^ 2] ^ 1 / 2 = root 26

In the space rectangular coordinate system, given a (1,1,3), B (2, - 1,3), find the length of | ab |

Root 5

In the space rectangular coordinate system, given that the coordinates of a and B are a (2,3,5) and B (3,1,4), then the distance between these two points | ab|=______ ．

∵ the coordinates of a and B are a (2, 3, 5), B (3, 1, 4), | ab | = (3 − 2) 2 + (1 − 3) 2 + (4 − 5) 2, = 1 + 4 + 1 = 6, so the answer is: 6

In the space rectangular coordinate system, the number of points equidistant from point a (3,1,2) B (4, - 2, - 2) C (0,5,1) is, which points are they?

Let the coordinates of the points equidistant from the three points be (x, y, z)
(x-3)^2+(y-1)^2+(z-2)^2=(x-4)^2+(y+2)^2+(z+2)^2=(x-0)^2+(y-5)^2+(z-1)^2,
The formula is as follows
(1) x-3y-4z=5
(2) -3x+4y-z=6
The general formula is (19n, 1 + 13N, - 2-5n), and N is an integer

In the rectangular coordinate system, three points a (0,1) B (2,0) C (2,1.5) are known
Find (1) if there is a point P (a, 1 / 2) in the second quadrant, use the formula containing a to represent the area of the quadrilateral abop
(2) Under the condition of (1), is there a point P that makes the area of the quadrilateral abop equal to the area of △ ABC? If so, find the coordinates of point P. if not, explain the reason?

(1) S quadrilateral abop = s △ AOP + s △ AOB = (1 / 2) * |ao | * [(- a) + 2] = (2-A) / 2 (a)

In space rectangular coordinate system, find the points equidistant from three points (3,1,2), (4, - 2, - 2), (0,5,1)

There are infinitely many points equidistant from the three points in space. These points are on a straight line passing through the center of the circumscribed circle of the three points and perpendicular to the plane they determine

Let point m be a point on the z-axis, and the distance from point m to a (1,0,2) is equal to point B (1, - 3,1), then the coordinate of point m is ()
A. （-3，-3，0）B. （0，0，-3）C. （0，-3，-3）D. （0，0，3）

Let m (0, 0, z), because the distance from point m to point a (1, 0, 2) is equal to point B (1, - 3, 1), so (1-0) 2 + (0-0) 2 + (2-z) 2 = (1-0) 2 + (- 3 + 0) 2 + (1-z) 2, that is, 1 + (2-z) 2 = 10 & nbsp; + (1-z) 2, and the solution is Z = - 3. So the coordinates of M are (0, 0, - 3). So choose B