Known: differential equation y '' + y = f (x), two special solutions y (0) = 0, y '(0) = 1, f' '(x) + F (x) = - SiNx, find f (x) =? The final answer is f (x) = (xcosx + SiNx) / 2

Known: differential equation y '' + y = f (x), two special solutions y (0) = 0, y '(0) = 1, f' '(x) + F (x) = - SiNx, find f (x) =? The final answer is f (x) = (xcosx + SiNx) / 2

f''(x)+f(x)=-sinx
f(0)=0
f'(0)=1
The three equations are solved together

Solving differential equation: y '- y = - SiNx

First, the homogeneous linear differential equation is solved
dy/dx=y
lny=c+x
y=e^(x+c)
Constant variation
y=c(x)e^x
dy/dx=dc(x)/dx*e^x+c(x)*e^x
The original equation is brought in
dc(x)/dx=-sin(x)*e^(-x)
Integral on both sides at the same time
c(x)=-1/2(sin(x)+cos(x))*e^(-x)+c
Bring in
y=-1/2(sin(x)+cos(x))+c*e^x

What is the necessary and sufficient condition for M (x, y) DX + n (x, y) dy = 0 to be a total differential equation

Because both sides of the equation may reduce the common function factor, so there is a picture conclusion. It is the basis of many special cases in the book of ordinary differential equations

The positive integers are arranged according to the rule shown in the figure. If the ordered real number pair (m, n) is used to represent the nth number from left to right, what is (62,55)
one
2.3.
4.5.6.
7.8.9.10.

Let's talk about (m, 1) first
In this case, it is 1 + [1 + 2 + 3 ····· + (m-1)] = 1 + m (m-1) / 2
For example, (10,1) is 1 + 10 times 9 divided by 2 = 46
(4,1) is 1 + 6 = 7
Then (m, n) is 1 + m (m-1) / 2 + (n-1)
That is, (62,55) is 1 + 62x61 / 2 + 54 = 1946

What is the number of all integers whose absolute value is greater than 2 but less than 5
Write about the process
The answer is four. I know, but why add negative numbers

The number of integers whose absolute value is greater than 2 but less than 5 is plus or minus 3 and plus or minus 4, a total of 4

What does a straight bar per unit length in a compound bar chart represent

The compound bar chart is to use two unit lengths to represent the quantity of one. According to the quantity, draw different straight bars, and then arrange these straight bars in a certain order. It is easy to see the quantity of the two from the compound bar chart

The two boxes contain 260 candies. If 1 / 8 of box a is put into Box B, the number of candies in box a and Box B is 7:6, how many candies are there in bottle B?

Now box a accounts for 7 / 13 of the total number of two boxes
The original box a accounted for 7 / 13 (1-1 / 8) = 8 / 13
The original nail box: 260 △ 8 / 13 = 160 pieces
Original Box B: 260-160 = 100 boxes
If you don't understand, please ask

Urgent, urgent, urgent. It is known that the area of each tile is 80x80 cm, which is equal to 0.8 square meter

0.8x0.8 = 0.64 square meters, there is a floor tile calculator on our website, which needs 93 floor tiles. It is recommended to buy more as the loss quantity
I hope my answer can help you provided by Beijing noxai decoration

Fifth grade summer homework (math problems)
1. The area of a rectangle is 12 square centimeters, and its length and width are in whole centimeters. How many kinds of rectangles are there?
2. Write two numbers as required so that their greatest common factor is 1
Two are prime numbers: () and (); two are composite numbers: () and (); one is prime number and one is composite number: () and ()
3. Among the three numbers 7, 15 and 21, () is a prime number, () and () are coprime numbers, () is a factor of (), and the common factor of () and () is 3
4. The minute hand of a clock is 8 cm long. After one hour, what is the distance of the tip of the minute hand?
5. Two ninths of a meter is 1 meter (), 2 meters ()
6. Add 12 to four-thirds of the numerator. In order to keep the size of the fraction unchanged, the denominator should be ()
7. A and B cups of water, in which a cup has salt, in which a cup has 20 grams of salt and 100 grams of water; B cup has 30 grams of salt and 200 grams of water. Which cup of water is saltier?
Please help! Thank you!

1. The area of a rectangle is 12 square centimeters, and its length and width are in whole centimeters. How many kinds of rectangles are there? What kinds are there? / 12 312 / 12 64a: there are three kinds of rectangles, which are 1 × 12, 2 × 6, 3 × 4.2. Write two numbers according to the requirements, so that the greatest common factor of them is 1

The distance between the bottom of street lamp A and B is 30 meters. One night, when Xiaohua walked to the place 5 meters away from the bottom of street lamp B, he found that the top of his figure just touched the bottom of street lamp B. Xiaohua was known to be 1.5 meters tall, so he calculated the height of street lamp a

As shown in the figure, AC is the height of lamp a, De is Xiaohua's height, ab = 30m, be = 5m, de = 1.5m, ∵ AC ⊥ AB, de ⊥ AB, ∵ BDE ∽ BCA, ∵ deac = BEAB, i.e. 1.5ac = 530, the solution is AC = 9m