How to solve the differential equation (x ^ 2 + 1) y '' = 2XY '

How to solve the differential equation (x ^ 2 + 1) y '' = 2XY '

(x^2+1)y''=2xy'
y''/y'=2x/(x^2+1)
(lny')'=(ln(x^2+1))'
lny'=ln(x^2+1) + C1
y'=C2*(x^2+1)
y=C2*arctg(x)+C3
C1, C2 and C3 are undetermined constants

For the differential equation y '' + y = SiNx, when we use the method of undetermined coefficient of special solution to find its special solution y ^ *, why is the special solution so designed~

The general solution of Y '' + y = 0 is y = c1cocx + c2sinx
Because the right end is e ^ (0) * SiNx, the coefficient of X is 1, and the corresponding complex number 0 + I = I is the root
So let y * = x (acosx + bsinx)

Given the second order differential equation y '' + 2Y '+ 2Y = (e ^ - x) SiNx, the special solution is X
If the second order differential equation y '' + 2Y '+ 2Y = (e ^ - x) SiNx is known, its special solution is
The answer is X &; (e ^ - x) &; (asinx + bcosx)
My answer is that there is no multiplication of X in the front. I don't know where x comes from

You can also ask me questions here:

Does the sequence have a limit? Why? UN = nsin (n Wu / 2)

There is no limit, and the swing sequence with increasing absolute value has no limit

In the linear function y = - 2x + 3, - 2 〈 y 〈 3, what is the value range of X?

0

Why u = U1 + U2 in series circuit and u = U1 = U2 in parallel circuit?
Such as the question 'master please answer, the best detailed point-

Series connection means that the total voltage is equal to the algebraic sum of each voltage. In parallel connection, it means that each voltage is equal to the total voltage. For example, every socket in our house is in parallel connection, so they are equal to the total voltage of the ammeter. They are all 220 v

Given the function f (x) = x ^ 2-2x + 3, when x ∈ [- 1, a], the value range of a is y ∈ [2,6]?
I just worked out a can take 1

Analysis
f(x)=(x-1)²-1+3
=(x-1)²+2
So when x = - 1
f(x)=6
When y = 2, x = 1
therefore
a≥1
Because the function is monotonically decreasing in [- 1, a]

In parallel circuit, u = U1 = U2, what about electromotive force?
Electromotive force is not the work done by electrostatic force when unit positive charge is transferred from the negative side of power supply to the positive side through the inside of power supply?

Electromotive force refers to the voltage given by the power supply, which is constant, independent of the external circuit, and related to the internal chemical structure of the battery, so that it is stable at a voltage, and the internal can be understood as you said

In the linear function y = 1 / 5x-4, if - 5 ≤ x ≤ 5, then the value range of Y is

If - 5

In physical electricity, u = U1 + U2. What do U1 and U2 represent?
Characteristics of series circuit voltage: the total voltage of series circuit is equal to the sum of the voltages of all parts. U＝U1+U2

U stands for voltage, U1 and U2 should be the voltage of some two resistors in the title, and u is the sum of their voltages