How to judge whether the ordinary differential equation is linear or not? As the title ~ the best example! Why is m * [y (x)] '+ T * siny = 0 nonlinear? Our teacher said that because there is a function of Y, it is nonlinear

How to judge whether the ordinary differential equation is linear or not? As the title ~ the best example! Why is m * [y (x)] '+ T * siny = 0 nonlinear? Our teacher said that because there is a function of Y, it is nonlinear

Let's look at y, y ', y' ', that is, the degree of Y and the derivatives of Y, if they are all of degree 1, then they are linear, otherwise they are nonlinear y' '+ X & sup2; y + x = 0, linear X & sup2; y' + (x-1) y + SiNx = 0, linear (y ') & sup2; + x = 0, nonlinear y' + Y & sup2; + x = 0, Nonlinear m * [y (x)] '+ T * siny = 0

How to judge the linear relationship is true?
There are two sets of data, X (1 n) And Y (1 n) How to prove that they have a linear relationship_ i=k*X_ i+b+ε

Calculate the correlation coefficient r, and the calculation method is shown in the figure (click to view the large picture)
  
Correlation coefficient is an indicator of the degree of correlation between variables. The sample correlation coefficient is expressed by R, and the overall correlation coefficient is expressed by ρ. The range of correlation coefficient is [- 1,1]. | R | the larger the value is, the smaller the error q is, the higher the degree of linear correlation between variables is; the closer the value is to 0, the larger the Q is, the lower the degree of linear correlation between variables is
If there is a positive correlation, R is positive, r = 1 is a completely positive correlation; if there is a negative correlation, R is negative, and R = - 1 is a completely negative correlation. When there is a completely positive correlation or negative correlation, all the points are on the linear regression line; the more scattered the distribution of points on the linear regression line, the smaller the absolute value of R. when the number of cases is equal, the closer the absolute value of the correlation coefficient is to 1, the closer the correlation is; the closer it is to 0, When r = 0, there is no linear relationship between X and Y. generally, when | R | is greater than 0.75, the two variables have a strong linear correlation

It is proved that two partial derivatives of function f (x, y) = (lxyl) ^ 1 / 2 exist at point (0,0), but function f (x, y) is not differentiable at point (0,0)

If partial derivative exists, you only need to find the normal derivative. For example, if you want to find the derivative of X, because y = 0, when x approaches 0, the value is still 0
So is the partial derivative of Y
When (0,0) is nondifferentiable, it means that it tends to (0,0) in any way, and the values are not all the same. For example, if it approaches (0,0) in the form of x = y, it is not differentiable

It is known that the hyperbola x2a2 − y2b2 = 1 and the parabola y2 = 8x have a common focus F, and one intersection point of the two curves is p, | PF | = 5, then the two asymptote equations of the hyperbola are______ ．

Let P (m, n), from the definition of parabola, | PF | = 5 = m + 2, | M = 3. From the definition of hyperbola, | 5m − A2C = Ca, ｛ 53 − A22 = 2A, ｛ a = 1, ｛ B = 3, ｛ two asymptote equations are & nbsp; 3x ± y = 0, so the answer is 3x ± y = 0

Cylinder = diameter is 21.3 cm. Length is 51.4 cm. Density is 7.86. How much is it

Volume v = π R & sup2; H = 3.14 × 15.65 & sup2; × 51.4 = 39529.5cm & sup3; weight of cylinder: 39529.5 × 7.86 = 310701.96g = 310.7kg

Who has the multiplication division formula computation application question 100 urgent need!
Fourth grade, multiplication and division method to one-step formula calculation, application problem is not limited to a few steps

1. The farm tool factory has to produce 20640 small farm tools, half of which have been completed in 120 days. How many small farm tools are produced per day on average?
2. A shoemaking factory produces 3860 pairs of men's shoes, which is twice as much as that of women's shoes. How many pairs of women's shoes can be produced
3. To build a canal, 840 meters have been built, and 120 meters have not been built. How many times has it been built? (answer in two ways)
4. 38 militiamen practice shooting, hitting 1026 rings in total. How many rings does each militiamen hit on average? (answer in two ways)
5. The length of the railway from Nanjing to Jinan is 540 kilometers. A train leaves from Nanjing and arrives in 9 hours. How many kilometers does this train travel per hour on average

Let f (x) = (2-A) LNX + 1 / x + 2aX
(1) Let g (x) = f (x) - 1 / x, increase and increase on [1, + infinity), and find the value range of A
(2) When a is not equal to 0, find the simple increasing interval of F (x)

(1) If G (x) is simple increasing on [1, + ∞), then G '(x) = f' (x) + 1 / X & # 178; ≥ 0, that is, f '(x) ≥ - 1 / X & # 178;,
Since x ∈ [1, + ∞), then - 1 / X & # 178; ∈ [- 1,0], so f '(x) ≥ 0
f'(x)=(2-a)/x-1/x²+2a=[2ax²+(2-a)x-1]/x²=(2x-1)(ax+1)/x²≥0,
Since x ＞ 1, then x & # 178; ＞ 0,2x-1 ＞ 0
Therefore, when x > 1, ax + 1 ≥ 0 is constant, that is, a ≥ - 1 / X & # 178;
When a ≥ 0, it is obviously true
If a ＜ 0, - 1 / X & # 178; ∈ [- 1,0), then a ≥ 0, which is not consistent with the hypothesis, is discarded
(2) If we know x > 0 from F (x), then x & # 178; > 0
Let f '(x) ≥ 0, then (2x-1) (AX + 1) ≥ 0
When a < 0,
① When a ＜ - 2, - 1 / a ＜ 1 / 2, the single increment interval is (- 1 / A, 1 / 2)
② When - 2 ＜ a ＜ 0, 1 / 2 ＜ a ＜ - 1 / A, the single increase interval is (1 / 2, - 1 / a)
③ When a = - 2, f '(x) = - (2x-1) &# 178 / X & # 178; ≤ 0, the simple increasing interval is & # 8709;
When a ＞ 0, - 1 / a ＜ 1 / 2, so x ＜ - 1 / A or X ＞ 1 / 2, also known as X ＞ 0, so the simple increasing interval is (0,1 / 2)

How many cubic meters of oxygen does a cubic meter of air contain
The air contains 21% oxygen. How many cubic meters of oxygen does 1 cubic meter of air contain?

21 cubic meters, because the gas fraction is calculated by volume, not by mass

For non-zero rational numbers a and B, the following operations are defined: a * b = B-1 of a, then (- 4) * 3 (- 2) = what

1

What is the area formula of a sphere?

The surface area of the sphere s = 4 π R & sup2; = π D & sup2; (R is the radius of the sphere, D is the diameter of the sphere)