Find the general solution of (1 + x2) dy + (1 + Y2) DX = 0

Find the general solution of (1 + x2) dy + (1 + Y2) DX = 0

The idea of upstairs is good, but there is a wrong symbol:
(1+x^2)dy=－(1+y^2)dx
Separation of variables
dy/(1+y^2)=－dx/(1+x^2)
Two sides integral
arctany=－arctanx+C
This place is the simplest
If you insist on solving y, you can
y=tan(－arctanx+C)

The general solution of the differential equation XDY YDX = y ^ 2dy

There is a simple solution
XDY YDX = y ^ 2dy deformation: (XDY YDX) / y ^ 2 = dy
Because: D (x / y) = (YDX XDY) / y ^ 2
So: D (x / y) = - dy
The general solution is: X / y = - y + C
Or: x = y (c-y)

Find the integral factor and general solution of differential equation YDX XDY = 0

dy/y=dx/x
Two sides integral
lny=lnx+C1
y=Cx

If the ordinal pairs (3a-1,2b + 5) and (8,9) have the same position, find the values of a and B

（3a-1=8 2b+5=9） a=3,b=2

The complex z = - 2 + 4I is a root equation of quadratic equation with real coefficients

Because the quadratic equation of one variable is conjugate, so - 2 + 4I and - 2-4i are its solutions,
So the equation is X & # 178; + 4 + 20 = 0

The fruit shop has 450 kg of fruit. The quality of pears is 4 / 5 of that of apples and 6 / 7 of that of peaches. How many kg are peaches?

450× 4/5 ÷ 6/7
= 360 ÷ 6/7
=420 kg peaches

The opposite vertex angle of an angle is 30 degrees smaller than 2 times of its adjacent complementary angle. What is the degree of this angle?

The opposite vertex of an angle is equal to him
Let this angle be x degrees
Then the adjacent complement angle is 180-x degrees
So x = 2 (180-x) - 30
x=360-2x-30
3x=330
x=110
So the angle is 110 degrees

If the direction vector a of line L = (- 2,3,1) and a normal vector n of plane α = (4,0,1), then the sine value of the angle between line L and plane Z is

The projection of a in n direction: T = a · n / | n|
=(-2,3,1)·(4,0,1)/√17
=-7/√17
Let L and Z form an angle: β
Then: sin β = | t | / | a | = √ 14 / (2 √ 17)

Hongxing primary school organized students to line up for an outing. The walking speed was 1 meter per second. Teacher Wang at the end of the line arrived at the head of the line at the speed of 2.5 meters per second, and then returned immediately
At the end of the team, it took 10 seconds. How long is the team?
. no equations

Suppose the team length is 1
The time for the teacher to walk from the end of the team to the head of the team is 1 △ of the total time (2.5-1), and then the time for the teacher to walk from the head of the team to the end of the team is 1 △ of the total time (2.5 + 1). The total time is 10 seconds, so the total distance, that is, the length of the team is 10 ÷ (1 / 1.5 + 1 / 3.5) = 10.5 meters

It is known that the m-th square minus bracket (n-1) x + 1 of the polynomial 3x is the quadratic binomial of X, so we can find the value of M-N!

M = 2. N = 1, so it's equal to 1