Solve the differential equation: dy / DX = KY + B, find the function relation of Y with respect to X

Solve the differential equation: dy / DX = KY + B, find the function relation of Y with respect to X

dy/(ky+b)=dx
d(ky)/(ky+b)=kdx
Integral: ln|ky + b| = KX + C1
ky+b=Ce^(kx)

Dy / DX = - y, y (0) = - 100

Y '+ y = 0, the general solution is: y = CE ^ (- x), from Y (0) = - 100, get: C = - 100
The solution is y = - 100e ^ (- x)

To solve the differential equation: dy / DX = (P + μ mGy) / my (where p, m, G and μ are constants)

(UG + P / my) dy = DX, integral on both sides

The general solution of the differential equation (1 + x ^ 2) dy + 2xydx = 0 is

（1+x^2）dy+2xydx=0
（1+x^2）dy=-2xydx
1/y*dy=-2x/(1+x^2)*dx
Integral on both sides at the same time
∫1/y*dy=∫-2x/(1+x^2)*dx
ln|y|=-ln|1+x^2|+ln|c|
y=c/(1+x^2)
or
(1+x^2)y=c

The quadratic function y = x square - 4x + 2 is known
The quadratic function Y-X & # 178; - 4x + 2 is known
(1) Write out the axis of symmetry and vertex coordinates of the function image
(2) Draw the function image
(3) According to the image, when x is the value, y decreases with the increase of X, and when x is the value, y increases with the increase of X;
(4) Point out the maximum or minimum value of the function according to the image, and write its value
Additional points for drawing

Solution 1: the original function can be transformed into y = (X-2) ^ 2-2, so it is not difficult to get that the symmetry axis of the conic is x = 2, and the vertex is [2, - 2] 2: we all know that y = ax ^ 2 + BX + C = 0, when a > 0, the opening of the image is upward [otherwise, it is downward], so y = x ^ 2-2x + 2 image only needs to find the vertex

f(x)=(cosx)^2-2sinx,0

Is the derivative - 2sinxcosx-2cosx
-2sinxcosx-2cosx＝0
cosx(sinx+1)=0
cosx=0,sinx=-1
0

Kneel down and ask for more than 1000 plus and minus calculation questions, no less than 1000, try your best

This is 1000

When x ∈ [0,1], find the minimum value of F (x) = x2 + (2-6a) x + 3a2

The axis of symmetry of the function is x = 3a-1. ① when 3a-1 ＜ 0, that is, a ＜ 13, Fmin (x) = f (0) = 3a2; ② when 3a-1 ＞ 1, that is, a ＞ 23, Fmin (x) = f (1) = 3a2-6a + 3; ③ when 0 ≤ 3a-1 ≤ 1, that is, 13 ≤ a ≤ 23, Fmin (x) = f (3a-1) = - 6A2 + 6a-1. In conclusion, the minimum value of the function is: when a ＜ 13, Fmin (x) = f (0) = 3a2, and when a ＞ 23, Fmin (x) = f (1) ）=When 13 ≤ a ≤ 23, Fmin (x) = f (3a-1) = - 6A2 + 6a-1

It is known that the two solutions of binary linear equations ax by = 5 are {x = 1, y = - 1 and {x = 2, y = 3,

The absolute value of the difference between the number of one digit and the number of hundred digit is equal to the number of eight

A total of 210, too many, can not be listed. I program out, it should be right