General solution of differential equation y '= (x + y) ^ 2

General solution of differential equation y '= (x + y) ^ 2

Let x + y = P, 1 + dy / DX = DP / DX, then
dp/dx-1=p^2,dp/dx=1+p^2,dp/(1+p^2)=dx
Arctanp = x + C, P = Tan (x + C), i.e
X + y = Tan (x + C) is the general solution

The general solution of the differential equation y '- Y / x = 0 is

dy/dx=y/x
dy/y=dx/x
ln|y|=ln|x|+c1
y=cx

Decompose the following factors into 1.9a & # 178; - 4B & # 178; 2.4x & # 178; - 25y & # 178; 3. A & # 178; X & # 178; + 16ax + 64

1、9a²-4b² =(3a)²-(2b)²=(3a+2b)(3a-2b)2、 4x²-25y² =(2x)²-(5y)²=(2x+5y)(2x-6y)3、a²x²+16ax+64=(ax)²+2×2a×8+8²=(ax+8)²

How to solve binary quadratic equations
Xy = negative half
x+y=2

First, replace one variable with another
If x + y = 2, then y = 2-x
Substitute another formula
Xy = negative half, X (2-x) = negative half
It's twice a dollar. Well, it's solved!
Don't understand can ask, help to please adopt!

(a + 1) x & # 178; - 2x + A-1 = O is a linear equation of one variable with respect to x, then a = ()

-1 because a + 1 = 0 can be one dollar at a time

It is known that the fourth moment a is similar to B: if the matrix is the eigenvalue 12, 13, 14, 15 of a, then the determinant | b-1-e|=______ ．

∵ the fourth moment a is similar to B, a and B have the same eigenvalues, that is, the eigenvalues of B are 12, 13, 14, 15, and the eigenvalues of B and B-1 are reciprocal, the eigenvalues of B-1 are 2, 3, 4, 5, so the eigenvalues of b-1-e are 2-1, 3-1, 4-1, 5-1, that is, 1, 2, 3, 4, so | b-1-e | = 1 × 2 × 3 × 4 = 24

3M and 178; N + 5MN and 178; + 6nm and 178; - 4N and 178; M-N and 178; m
（1）3m²n+5mn²+6nm²-4n²m-n²m
（2）2/3a²-6a³＋5a-1/4+5a³-1/2-4/3a²
fast

（1）3m²n+5mn²+6nm²-4n²m-n²m=(3m²n+6nm²)+(5mn²-4n²m-n²m)=9m²n（2）2/3a²-6a³＋5a-1/4+5a³-1/2-4/3a²=(2/3a²-4/3a²)-(6a...

If 4x + 8 = 32, then 6x + 0.5 = ()

4x=32-8
4x=24
x=24/4
x=4
6*6+0.5=36.5
thirty-six point five

The known function f (x) = 4x ^ 2-7 / 2-x, X ∈ [0,1]
(1) Finding monotone interval and range of F (x)
(2) Let a ≥ 1 function g (x) = x ^ 3-3a ^ 2x-2a, X ∈ [0,1] exist for any x ∈ [0,1], let g (x) = f (x) hold, and then find the value range of A

(1) F '(x) = [8x (2-x) + (4x ^ 2-7)] / (2-x) ^ 2 = (- 4x ^ 2 + 16x-7) / (2-x) ^ 2 = - (2x-7) (2x-1) / (2-x) ^ 2 x ∈ [0,1] when 1 / 2 = 1, when x > A, G' (x) > 0, G (x) increases when - A0, G (x) increases when x = - A, G '(x) = 0, G (x) is maximal when x = a, G' (x) = 0, G (x) is minimal, X ∈ [0,1], a > = 1, G (x) is simple

Given the inverse scale function y = - 6 / x, when y = 6, find the value of X? When y is less than or equal to 6, find the value range of X?

y=-6/x
6=-6/x
x=-1
-6/x=y=0
x(x+1)>=0
x0