The general solution of differential equation XDY / DX + y = YLN (XY) is solved by variable transformation

The general solution of differential equation XDY / DX + y = YLN (XY) is solved by variable transformation

Let u = ln (XY) = LNX + LNY
du=dx/x+dy/y
The original formula is dy / y + DX / x = ln (XY) DX / X
du=udx/x
du/u=dx/x
We get u = Cx
ln(xy)=Cx

What is the solution of the differential equation XY ′ + y (LNX LNY) = 0 satisfying the condition y (1) = e ^ 3?

dy/dx=y/xln(y/x)
Let Y / x = u, y = UX
dy/dx=xdu/dx+u
xdu/dx+u=ulnu
1/u(lnu-1)du=1/xdx
∫1/u(lnu-1)du=∫1/xdx
∫1/(lnu-1)d(lnu-1)=ln|x|+ln|c|
ln|lnu-1|=ln|x|+ln|c|
lnu-1=cx
lny/x-1=cx
y/x=e^(cx+1)
y=xe^(cx+1)
e^3=e^(c+1)
c=2
therefore
The special solution is: y = Xe ^ (2x + 1)

Given the set a = {X - 2 ≤ x ≤ a}, B = {y y = 2x + 3, X ∈ a}, C = {Z Z = x ^ 2, X ∈ a}, if a ∩ B = a, find the value range of A

, B = {y y = 2x + 3, X ∈ a},
So - 1 ≤ y ≤ 2A + 3
A ∩ B = a, so a is a subset of B
a≤2a+3
The solution is a ≥ - 3
And because - 2 ≤ x ≤ a
So a ≥ - 2
So a ≥ - 2

① 4x2 / 5 / 1 / 3 / 1, 15 / 16 / 2 / 3-4 / 1, 2.5x (2 / 5-1 / 3) + 2.1
④ 2 out of 15 (1.1-3 out of 4) + 1 out of 5 x 5 out of 3 will be answered today to bless your happiness
We need the formula!

① 4 / 5 x 2 / 1 / 3
=2/5÷1/3
=6/5
=1.2
② 15 / 16 △ 3 / 2-1 / 4
=5/8-1/4
=3/8
③ 2.5x (2 / 5-1 / 3) + 2.1
=2.5×1/15+2.1
=1/6+2.1
=2 and 4 / 15
④ 2 / 15 ÷ (1.1-3 / 4) + 1 / 5 x 5 / 3
=2/15÷0.35+3/25
=8/21+3/25
=263/525

If the lengths of two sides of a right triangle are 6 and 8 respectively, and the lengths of another right triangle similar to it are 3 and 5 and X respectively, then the value of X ()

If the two sides of a right triangle are 6 and 8, the hypotenuse is 10,
Because 3:6 = 5:10
So x and 8 are the corresponding edges,
So x = 4,

Solving equation x-0.4 = 12 12 (x + 3.7) = 144 5x-3 * 11 = 42 8x-6 = 42 (checking calculation)
X-0.4 = 12 12 (x + 3.7) = 144 5x-3 * 11 = 42 8x-6 = 42 (checking calculation)

X-0.4 = 12, x = 12 + 0.4, x = 12.4 checking calculation: when x = 12.4, 12.4-0.4 = 12; 12 (x + 3.7) = 144 (x + 3.7) = 144 / 12 (x + 3.7) = 12, x = 12-3.7, x = 8.3 checking calculation: when x = 8.3, (8.3 + 3.7) * 12 = 12 * 12 = 144, the result is positive

What is the tangent equation of curve y = x ^ 2 + 3 at point (1,4)?

y = x^2 + 3
y' = 2x
At point (1,4), y '= 2 * 1 = 2, that is, tangent slope k = 2
So the tangent equation: Y - 4 = 2 (x - 1)
It is reduced to y = 2x + 2

Rational number is the general name of positive integer, negative integer, positive fraction and negative fraction, right?

Integers and fractions are called rational numbers. Any rational number can be written in the form of fraction M / N (m, n are all integers, and N ≠ 0). Infinite acyclic decimals and numbers with endless open roots are called irrational numbers, such as π, 3.1415926535897932384626

Find the extremum and extremum of function f (x) = x & # 178; / X & # 178; + 3

f'(x)=[2x(x^2+3)-x^2(2x)]/(x^2+3)^2
=[2x^3+6x-2x^3]/(x^2+3)^2
=6x/(x^2+3)^2
x> When f '(x) > 0, the function increases monotonically, X

If the product of a number and its reciprocal plus the reciprocal of a is nine eighths, find the reciprocal of A

The product of a number and its reciprocal is 1
So the question becomes 1 plus the reciprocal of a is nine eighths, so the reciprocal of a = 9 / 8-1 = 1 / 8