The function y = CX ^ 3 is a differential equation____ The general solution of the problem

The function y = CX ^ 3 is a differential equation____ The general solution of the problem

y - (1/3) * x * dy/dx = 0
By y = C x ^ 3
Find dy / DX = 3C x ^ 2
And then take the equation of X or something

It is proved that y = C1 * e ^ (C2 - x) - 1 is the solution of the differential equation y "- 9y = 9, but not the general solution. C1 and C2 are arbitrary constants

The general solution is y = C1 e ^ 3x + C2 e ^ (- 3x) - 1

The general solution is (x-c1) ^ 2 + (y-c2) ^ 2 = 1 differential equation, and the answer is (y ')) ^ 2 = [(y') ^ 2 + 1] ^ 3,

∵ (x-c1) ^ 2 + (y-c2) ^ 2 = 1 = = > 2 (x-c1) + 2 (y-c2) y '= 0 (both ends of the equation are derived from x) = = > x-c1 - (1 + (y') ^ 2) y '/ Y "= 0 (both ends of the equation are derived from x) ∵ (1) x-c1 = (1 + (y') ^ 2) y '/ Y". "(1) x-c2 = - (1 + (y') ^ 2) / Y"; (2) substituting (1) and (2) into the general solution, we get ((1 + (y ') ^ 2) y

It is proved that if the positive series ∑ UN converges, then ∑ UN ^ α (α > 1) converges

∵limUn=0
lim(Un^a/un)=lim(un^(a-1))=0
If the positive series ∑ UN converges, then ∑ UN ^ α (α > 1) converges

Is the series UN ^ 2-un + 1 ^ 2 convergent

Divergence
un→0
un^2-un+1/2→1/2
According to the necessary condition of series convergence,
Divergence of series ∑ (UN ^ 2-un + 1 / 2)

Let ∑ (UN + UN + 1) be convergent

This problem investigates two properties of series: 1. Arbitrarily adding or removing the finite number of series does not change its convergence
2. If the series ∑ an converges and ∑ BN converges, then the series ∑ (an + BN) also converges
The general term is divided into two parts: UN and U (n + 1). It is known that ∑ UN converges, but ∑ U (n + 1) only has one term U1 less than ∑ UN. Removing the finite term of the series does not change the convergence, so ∑ U (n + 1) converges, and ∑ (UN + U (n + 1)) converges by using the properties of the series

If Limun = 0, then the series ∑ UN converges

Not necessarily, in addition to the limit, there is also the domain of definition to determine the convergence of an inclusion number

It is proved that ∑ UN is divergent and ∑ u2n is divergent

Un=1+（-1）^(n+1)

How much does {UN} converge to a and {UN + 1} converge to

Let {UN} converge to A. We can see that there is a constant K (k is greater than 2), when n is greater than k, | uk-a | is less than S. so another sequence yn = UN + 1, so: | (YK-1) - a | is less than S. then we can prove that there is a constant (k-1), so that the sequence yn has

In a parallel circuit, is the power supply voltage equal to the voltage on both sides of the parallel appliance? Then why is U1 = U2 = u different from U1 + U2 = u in the current

In a parallel circuit, is the power supply voltage equal to the voltage on both sides of the parallel electric appliance? Yes, U1 = U2 = u - this is the voltage relationship of the parallel circuit