How to calculate (1 + X * x) dy = (1 + XY) DX y|x = 0 = 1

How to calculate (1 + X * x) dy = (1 + XY) DX y|x = 0 = 1

(1 + X * x) dy = (1 + XY) DX y | x = 0 = 1 it is observed that y = x is the special solution of the equation. In order to find the general solution, let y = x + T, substitute it into the original equation to get (1 + X ^ 2) (1 + T ') DX = (1 + x ^ 2 + XT) DX, and simplify it to DT / T = xdx / (1 + x ^ 2). Therefore, t = C (1 + x ^ 2) ^ (1 / 2) so, y = x + C (1 + x ^ 2) ^ (1 / 2) x = 0 = 1, so y = 1

How many cubic meters is one ton of oil

The specific gravity of oil is about 0.9, because I don't know what oil you are talking about, so let's take it as 0.9
Therefore, one cubic meter is 0.9 tons
1 / 0.9 = 1.11m3

How to do the complete square formula? It's better to give some examples

^It means square
(a+b)^2=a^2+2ab+b^
such as
（3+2）^
=3^+2（3*2）+2^
=9+12+4
=25

Calculate ∫ ∫ ∫ zdxdydz, where Ω is the closed region bounded by the cone z = h * (x2 + Y2) / R under the root sign) and the plane z = H (r > 0, H > 0)
∫0 2πdθ ∫0 Rρdρ ∫hρ/R h zdz
Why not

You should put the correct answer up for others' reference. I think it's right

How many meters per second is 100 kilometers per hour

100 * 1000 m / 60 * 60 s = 250 / 9, about 27.78 M / s

67 * 65 / 66 + 1 / 66 simple calculation
67 times 65 out of 66 plus 1 out of 66

67 × 65/66 + 1/66
=（66 +1）×65/66 + 1/66
=65 + 65/66 +1/66
=65 + 1
=66

Given that the diameter of the bottom of the cylinder is 2K, a plane with an angle of 30 ° to the bottom cuts the cylinder, then the eccentricity of the ellipse on the section is_____

The length of the major axis of the ellipse cut at 30 ° is 2K / cos 30 ° and the length of the minor axis is 2K, so a = 2 (3) K / 3, B = K. C = 3 / 3, e = 1 / 2

The area of a rectangle is a (2a + b) + B (2a + b), and the length and width are calculated

First, we extract the common factor and get s = (2a + b) (a + b) because 2A + b > A + B, the length is 2A + B and the width is a + B

Factorization: 2x ^ 4-x ^ 3 + 6x ^ 2-x + 6

2x4-x3-6x2-x+2 =x^2(2x^2-x-6)-(x-2)=x^2(2x+3)(x-2)-(x-2)=(x-2)[x^2(2x+3)-1]=(x-2)(2x^3+3x^2-1)=(x-2)[(2x^3+2x^2)+(x^2-1)]=(x-2)[2x^2(x+1)+(x+1)(x-1)]=(x-2)(x+1)(2x^2+x-1)=(x-2)(x+1)(2x-1)(x+1)=(x+1)^2...

Given two points a (- 2,0), B (0,2), and point C is any point on the circle x2 + y2-2x = 0, then the minimum area of △ ABC is ()
A. 3-2B. 3+2C. 6−22D. 3−22

The equation of straight line AB is x − 2 + y2 = 1, that is, X-Y + 2 = 0, circle x2 + y2-2x = 0, which can be reduced to (x-1) 2 + y2 = 1, the distance from the center of circle (1,0) to the straight line is d = | 1 − 0 + 2 | 2 = 322, the minimum distance from the point on the circle to the straight line is 322 − 1 ∵ | ab | = 22, and the minimum area of ABC is 12 × (322 − 1) × 22 = 3 − 2, so a is selected