General solution of homogeneous differential equation (y2-3x2) dy + 2xydx = 0

General solution of homogeneous differential equation (y2-3x2) dy + 2xydx = 0

（y^2-3x^2）dy+2xydx=0
y^2dy+(2xydx-3x^2dy)=0
Divide by Y ^ 4:
dy/y^2+(2xydx-3x^2dy)/y^4=0
dy/y^2+d[x^2/y^3]=0
Tong-1 / y + x ^ 2 / y ^ 3 = C
Or: y ^ 2-x ^ 2 = CY ^ 3

What is the general solution of the ordinary differential equation 2xydx + (x ^ 2-y ^ 2) dy = 0

2xydx+(x^2-y^2)dy=0
2xydx+x^2dy-y^2dy=0
d(x^2y)-d(y^3/3)=0
The general solution is: x ^ 2y-y ^ 3 / 3 = C

Try to explain the graph represented by the set of points (x, y, z) satisfying the equation x = 1 and 1y = 1 in the space rectangular coordinate system
Can you be more precise

A line parallel to the z-axis

As shown in Figure 1, it is known that the images of positive scale function and inverse scale function pass through the points m (- 2, - 1), and P (- 1, - 2) is a point on the hyperbola, q is a moving point on the coordinate plane, PA is perpendicular to the X axis, QB is perpendicular to the Y axis, and the perpendicular feet are a and B respectively
(1) (2) when the point Q moves on the line Mo, is there such a point Q on the line Mo that the area of △ OBQ is equal to that of △ OAP? (3) as shown in Figure 2, when the point Q moves on the hyperbola in the first quadrant, make the parallelogram opcq with OP and OQ as the adjacent sides, and find the minimum perimeter of the parallelogram opcq

(1) Let the analytic expression of positive proportion function be y = KX, substituting the coordinates of point m (- 2, - 1) into k = 12, so the analytic expression of positive proportion function is y = 12x, and the analytic expression of inverse proportion function is y = 2x; (2) when point Q moves on the straight line OM, let the coordinates of point Q be q (m, 12m), then s △ OBQ = 12ob · BQ =

How to understand a sign before a negative number

Negative is positive
If 1 is the opposite of - 1, then - 1 is the opposite of - (- 1)
And 1 and - 1 are opposite numbers, so - (- 1) = 1

It is known that the quadratic function f (x) satisfies f (x-1) - f (x) = 2x + 3 and f (0) = 1
(1) Finding the analytic expression of F (x) (2) finding the domain of definition and value of F (x)

(1) Let f (x) = ax ^ 2 + BX + C, then: F (x-1) - f (x) = a (x-1) ^ 2 + B (x-1) + C - (AX ^ 2 + BX + C) = - 2aX + a-b-2ax + A-B = 2x + 3, a = - 1, B = - 4, f (0) = C = 1F (x) = - x ^ 2-4x + 1 (2). Obviously, the domain of definition is r, f (x) = - x ^ 2-4x + 1 = - (x + 2) ^ 2 + 5, so the range is [5, positive infinity]

A + A + A + A + a omit multiplier sign

a+a+a+a+a =5a

What are imaginary numbers and real numbers collectively called?

Plural
Complex number: is the general name of real number and imaginary number. The basic form of complex number is a + bi, where a and B are real numbers, a is real part, Bi is imaginary part, I is imaginary unit. On the complex plane, a + bi is point Z (a, b). Real number: the general name of complex number, rational number and irrational number without imaginary part

What is the ideal condition of linear regression equation of one variable?

1) Linear correlation
2) There is a significant correlation between the two variables
3) There are enough known data, and the independent variables and dependent variables are clear
4) The random error values are independent of each other and have the same variance,
 random error ~ n (0, σ 2)

The maximum area of the inscribed rectangle of the ellipse x24 + y2 = 1 is______ ．

Let y = kxx24 + y2 = 1, change to (1 + 4k2) x2 = 4, take the vertex a (x, y) of the first quadrant, and get x = 21 + 4k2, y = 2K1 + 4k2. The area of inscribed rectangle s = 2x · 2Y = 4xy = 4 × 4k1 + 4k2 = 161k + 4K ≤ 1621k · 4K = 4 =So the maximum area of the inscribed rectangle of the ellipse x24 + y2 = 1 is 4