General solution of differential equation (x2 + Y2) DX = xydy X2 is the square of X

Let: u = Y / X
Then: y = Xu dy / DX = u + XDU / DX
By: (x ^ 2 + y ^ 2) DX = xydy
dy/dx=(x^2+y^2)/xy=x/y + 1/[x/y]
dy/dx=u+xdu/dx=u+1/u
xdu/dx=1/u
udu=1/x dx
1/2 u^2=ln|x| +c1
u=y/x= [ln(x^2) +c)]^(1/2)
y=x[ln(x^2) +c)]^(1/2)

General solution of differential equation XDY / dx-y = x2 + Y2
2 is the square~

xdy/dx-y=x^2+y^2
（x^2+y^2+y)dx-xdy=0
Let P (x, y) = x ^ 2 + y ^ 2 + y, q (x, y) = - X
P for y = 2Y + 1, q for x = - 1
Inequality, the original equation is not a total differential equation
The original equation can be reduced to: (x ^ 2 + y ^ 2) DX + YDX XDY = 0
It can be seen from the observation that 1 / (x ^ 2 + y ^ 2) is its integral factor, and both sides of the original equation multiply by 1 / (x ^ 2 + y ^ 2), and the equation becomes
dx-(xdy-ydx)/(x^2+y^2)=0
The general solution of the original equation is obtained by integrating both sides
x-arctan(y/x)=C y=xtan(x-C)

(1 / 3) parachutists perform low altitude parachuting. The plane flies 224m above the ground. The parachutists leave the plane to do free fall in the vertical direction
(1 / 3) parachutists perform low altitude parachute jumping. The plane flies 224m above the ground horizontally. The athletes leave the plane to do free fall in the vertical direction. After a period of time, they immediately open the parachute and open the parachute

1.
5^2-v^2=-2*h*12.5
2*(224-h)*g=v^2
The simultaneous solution is: H = 99m, v = 50M / s
That is, 99 meters above the ground to expand the umbrella
two
125m=0.5gt1^2
T1 = 5S / time before parachute opening/
T2 = (v-vo) / a = (50-5) / 12.5 = 3.6s/time after parachute opening/
The shortest time in the air: T = 5 + 3.6 = 8.6s

How many ninths are there in five ninths, that is, how much is one minus five ninths?

Five, one is nine, one in nine, four in nine

The maximum static friction is greater than sliding friction,

In fact, it is an empirical fact that the maximum static friction is greater than the sliding friction, which is obtained and verified from experience as well as the vector algorithm, At present, there is no theoretical deduction. I think the theoretical deduction in the book should refer to the principles in physics and the definition deduction in mathematics. The conclusion obtained through strict proof is that the definition of friction exists only at the macro level, so it is difficult to explore it in depth. The most intuitive explanation method is the idea of magnification. As shown in the figure, the contact surface of two objects causing friction is magnified, It is easy to draw the schematic diagram in the figure above. It is not difficult to see that when the maximum static friction is from motionless to motional, the work to be done is to extrude the deformed rough surface tangentially to the deformation degree. On the basis of the deformation of the contact surface, the sliding friction only needs to overcome the deformed rough particles, Static friction should be greater than sliding friction, but the word "slightly" can not give a good quantitative explanation_ (laughter)~

If the equation 3xa-1 + 9 = 0 is a linear equation of one variable with respect to x, then a = ()

If you have X to the power of a, then a = 1
If you multiply 3x by a here, then a ≠ 0
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It takes 12 hours for a car to go back and forth between a and B. It takes 45km per hour from a to B and 30km per hour to return
A. B how many km is the distance between the two places?

Let the time to go be a hour
According to the meaning of the title
45：30=（12-a）：a
45a=30×12-30a
45a+30a=360
75a=360
A = 4.8 hours
Then AB distance = 45 × 4.8 = 216 km

The size of 2006 in 2007 and 2007 in 2008

1-2006/2007=1/2007
1-2007/2008=1/2008
As 1 / 2007 > 1 / 2008
therefore
2006 of 2007 < 2007 of 2008

Calculate 1 + 2 + 3 + 4 + 5 + 6. + 998 + 999 =?

50000

General solution of differential equation (x2 + Y2) DX = xydy X2 is the square of X