General solution of homogeneous differential equation xdy-y (LNY LNX) DX = 0

General solution of homogeneous differential equation xdy-y (LNY LNX) DX = 0

By transforming dy / DX = y (LNY LNX) / x = Y / X * ln (Y / x) and substituting Y / x = py = PXY '= P + p'x into the original equation, P + p'x = plnp, DP / [P (lnp-1)] = DX / xed (P / E) / ln (P / E) = DX / x, e * lnln (P / E) = LNX + C, that is, e * lnln (Y / ex) = LNX + C

The general solution of XDY - [y + XY ^ 3 (1 + LNX)] DX = 0

Let z = 1 / Y & # 178;, then dy = - Y & # 179; DZ / 2 be substituted into the original equation, and then XDZ + 2zdx = - 2x (1 + LNX) DX = = > X & # 178; DZ + 2xzdx = - 2x & # 178; (1 + LNX) DX = = > d (X & # 178; Z) = - 2x & # 178

General solution of differential equation XDY YDX = x / LNX * DX

xdy-ydx
=x^2 * (xdy-ydx)/x^2
=x^2* d(y/x)
Divide both sides by x ^ 2
That is: D (Y / x) = 1 / (x * LNX) DX
y/x= ln(lnx)+C
y= xln(lnx)+Cx

Can the tolerance of arithmetic sequence be zero?
What about the equal ratio sequence?

Of course, zero tolerance is a constant column

In rectangle ABCD, ab = 4, ad = 3, PA ⊥ ABCD, PA = √ 3, then the size of dihedral angle p-dc-a is

Even PD, dihedral angle p-dc-a is ∠ PDA
If ad = 3, PA = √ 3, then PD = 2 √ 3
Special triangle. PDA = 30 degree

The function f (x) = 4x ^ 2-2 (P-2) x-2p ^ 2-P + 1 has at least real number C in the interval [- 1,1]. What is the negation of F (c) > 0?
I want the negation of proposition,

There is at least one point C such that f (c) > 0, that is to say, the maximum value > 0. For quadratic functions, f (x) = 4x & sup2; - 2 (P-2) x-2p & sup2; - P + 1 has the opening upward, so the maximum value is taken as f (- 1) = - 2p & sup2; + P + 1, f (1) = - 2p & sup2; - 3P + 9 at the end. The axis of symmetry of the function is (P-2) / 4 when (P-2) / 4

The plane equation passing through point (1,3,0) and passing through line X-1 / 3 = y + 3 / - 2 = Z + 2 / 1

The plane equation of X-1 / 3 = y + 3 / - 2 = Z + 2 / 1
x-1/3=y+3/-2
-2(x-1)=3(y+3)
2x+3y+7=0
x-1/3==z+2/1
x-1=3z+6
x-3z-7=0
Let all plane equations be
2x+3y+7+a(x-3z-7)=0
Another point (1,3,0)
Namely
2+9+7+a(1-0-7)=0
6a=18
a=3
therefore
The equation is
2x+3y+7+3(x-3z-7)=0
Namely
5x+3y-9z-14=0

How to do factorization of polynomial 2A + 4AB + 2b-8c

2A + 4AB + 2B - 8C
=[(2a & # 178; + 4AB + 2B & # 178;) - 8C & # 178;] (four factorizations must be grouped first)
=【2(a+b)²-8c²】
=2【（a+b)²-4c²】
=2(a+b-2c)(a+b+2c)

As shown in the figure, in the cube abcd-a1b1c1d1, the tangent of the dihedral angle b-a1c1-b1 is___ ．

Let D1 be the origin, d1a1 be the x-axis, d1c1 be the y-axis, d1d be the z-axis, and establish the rectangular coordinate system of d1-xyz space. Let the side length of the cube be 1, and it is easy to know that a normal vector of plane a1c1b1 is (0, 0, 1). Let A1 (1, 0, 0), B (1, 1, 1), C1 (0, 1, 0), then vector A1B = (0, 1, 1), vector C1b = (1, 0, 1) and then let plane ba1c1 be a square If a normal vector is (x, y, z), the solution can be (1, 1, - 1). From the two normal vectors, the cosine value of the dihedral angle b-a1c1-b1 is 33, and then from the triangular relationship, the tangent value of the dihedral angle b-a1c1-b1 is 2

Speed, arrange the natural number 1 100 in the following table. In this table, use two lines of six numbers in the square box
Arrange the natural number 1 100 in the following table. In this table, use two rows of six numbers in the square frame. If the sum of the six numbers in the frame is 429 (10 11 12 13 17 18 19), what is the smallest of the six numbers
1 2 3 4 5 6 7
8 9 10 11 12 13 14 omitted

Let the smallest of the six numbers in the frame be a (the number in the top left corner of the rectangular box), then the other two numbers in the upper row are a + 1 and a + 2, and the three numbers in the next row are a + 7, a + 8, a + 9. According to the meaning of the question: a + A + 1 + A + 2 + A + 7 + A + 8 + A + 9 = 429, a = 67 is the smallest of the six numbers