The general solution of the differential equation y '+ ysinx = e ^ (- cosx)

The general solution of the differential equation y '+ ysinx = e ^ (- cosx)

∵ homogeneous equation y '+ ysinx = 0 = = > y' = - ysinx
==>dy/y=-sinxdx
==>LNY = cosx + LNC (C is an integral constant)
==>y=Ce^cosx
The homogeneous equation is y = CE ^ cosx (C is an integral constant)
Therefore, let the general solution of the original differential equation be y = C (x) e ^ cosx (C (x) denotes a function of x)
∵y'=C'(x)e^cosx-C(x)sinxe^cosx
Substituting into the original equation, C '(x) e ^ cosx = e ^ cosx
==>C'(x)=1
==>C (x) = x + C (C is an integral constant)
∴y=C(x)e^cosx=(x+C)e^cosx
So the general solution of the original differential equation is y = (x + C) e ^ cosx (C is an integral constant)

The general solution of y'cosx + ysinx = 1

Y '+ P (x) y = q (x) corresponding formula is y = e ^ (- ∫ P (x) DX) [∫ Q (x) e ^ (∫ P (x) DX) DX + C]

If vector A / / vector B and LAL = 1, LBL = 2, then A.B=
That part of the conditions
2. In the same plane rectangular coordinate system, the number of intersections between the image of function y = cos (x / 2 + 3 / 2 π) and the line y = 1 / 2

According to the induction formula, y = sin (x / 2), visualize it and y = 1 / 2, and you will find that they have countless intersections
The first respondent used the wrong induction formula, and the second respondent's answer was too cumbersome

72 / (16-x) = 3 / 5 4x + 1 / 2 × 3 / 4 = 13.1x + 0.8 = 10.1
What is the sum of a number and 4 / 3 × 5 / 8 equal to 23 / 24
3 / 4 of the number a is 84, and 3 / 4 of the number B is 84. How much is the number a larger than the number B?
72 / (16-x) = 3 / 5
4X + 1 / 2 × 3 / 4 = 1
3.1x+0.8=10.1
Give the first satisfactory answer

72 / (16-x) = 3 / 5, 3 (16-x) = 36048-3x = 3603x = - 312x = - 1044x + 1 / 2 × 3 / 4 = 14x + 3 / 8 = 14x = 5 / 8x = 5 / 32 3.1x + 0.8 = 10.3.1x = 9.3x = 3, the sum of a number and 4 / 3 × 5 / 8 equals 23 / 24

Test of 0.6x-2.4 = 18 solution equation

0.6x-2.4=18
0.6x=2.4+18
0.6x=20.4
x=20.4/0.6
x=34

The positional relationship between the line 4x-3y = 50 and the circle x ^ 2 + y ^ 2 = 100 is (write the proof)
A intersects, B is tangent and C is apart

B
Substituting point (0,0) into equation (4x-3y-50) / 4 ^ 2 + 3 ^ 2, the result is compared with 10. If it is equal, the tangent is smaller and the intersection is more distant

Under what circumstances are calculators generally used

Help calculate a quadratic equation of one variable
7n^2-71n-25806=0

7n² - 71n - 25806 = 0
(n - 66)(7n + 391) = 0
N = 66 or n = - 391 / 7

What is the necessary and sufficient condition for the boundedness of functions and its proof

This question can be understood as follows:
Let f (x) be defined in the number set X. it is proved that f (x) is bounded on X if and only if it has both upper and lower bounds on X
Proof: sufficiency:
If f (x) is upper bound m and lower bound n
Then: | f (x) | a, f (a) - > ∞, then | f (a) | - > + ∞, then there is no a such that any x ∈ X has | f (x)|

The sum of integer solutions of equation | x-1002 | + | x + 1003 | = 2005 is

Because the absolute value can be seen as the distance on the number axis, that is, | x-1002 | can be seen as the distance to 1002, | x + 1003 | can be seen as the distance to - 1003, it can be seen on the number axis that only - 1003 ≤ x ≤ 1002 is in the range. Because the integers on this number axis cancel each other, only - 1003 is left, that is, - 1002 and 1002 offset, - 1001 and 1001 offset, etc., so the sum of integer solutions is - 1003