Given that the function y = [(x + 1) ^ 2] U (x) is the general solution of the equation y '- 2Y / (x + 1) = (x + 1) ^ 3, find u (x)

Given that the function y = [(x + 1) ^ 2] U (x) is the general solution of the equation y '- 2Y / (x + 1) = (x + 1) ^ 3, find u (x)

Substituting y = [(x + 1) & # 178;] U (x) into the equation, we can get: (x + 1) U '(x) = (x + 1) & # 179; therefore, u (x) = 1 / 3 (x + 1) & # 179; + C

The general solution of the equation y "- 2Y '- 3Y = 0 is obtained, and the special solution satisfying the initial conditions y (0) = 1 and y' (0) = 2 is obtained

Y "- 2Y '- 3Y = 0 corresponding to the equation of characteristic root: T ^ 2-2t-3 = 0, t = 3, or, t = - 1, then the general solution of the original equation is y = C1E ^ (3x) + c2e ^ (- x) y' = 3c1e ^ (3x) - c2e ^ (- x) y (0) = 1, y '(0) = 2, C1 + C2 = 1, 3c1-c2 = 2, C1 = 3 / 4, C2 = 1 / 4Y = 3 / 4E ^ (3x) + 1 / 4E ^ (- x)

Finding the general solution of differential equation y '= Y / (2x) + 1 / (2Y) Tan (y ^ 2 / x)

If we know that the sum of MX ^ 3Y ^ B. - 2x ^ a-1y ^ n-2.3x ^ C + 1y ^ 5 is 0, then what is a + B + c-m-n?

Since sum is zero, it must be of the same kind, just offsetting each other
If x is 3 = A-1 = C + 1, then a = 4 and C = 2
For y, if B = n-2 = 5, then B = 5, n = 7
For the coefficient m-2 + 3 = 0, M = - 1
So a + B + c-m-n = 4 + 5 + 2 - (- 1) - 7 = 5

It is known that the sum of - 4x ^ (m-2) y ^ 3 and 2x ^ 3Y ^ (7-2n) is still the monomial m ^ 2 + 2 ^ n =?

Because sum is still monomial
Then m-2 = 3
7-2n=3
m=5 n=2
m^2+2^n=5^2+2^2=25+4=29

It is known that 23x3m-1y3 and - 14x5y2n + 1 are similar terms, then the value of 5m + 3N is______ ．

∵ 23x3m-1y3 and - 14x5y2n + 1 are the same category, if ∵ 3m-1 = 5, 2n + 1 = 3, ∵ M = 2, n = 1, then 5m + 3N = 5 × 2 + 3 × 1 = 10 + 3 = 13

How to calculate the number of monomials
For example, 3A / BC

The concept of degree and coefficient of monomials and polynomials
[1] Monomials:
In general, it is said that all the monomials in front of what are called coefficients. For example, the monomials of XY; ABXY, the coefficients are ab
For example, for the monomial of XYZ: 3axyz, the coefficient is 3a, the number of times is XYZ, and the sum of exponents: 1 + 1 + 1 = 3 is cubic
[2] Polynomials
Polynomials are also composed of uninomials that cannot be merged. The degree of the highest degree of the polynomial is called the degree of the polynomial. For example, the polynomial 3ax3y2-3bx + 4ay2 about XY
His number is 3 + 3 = 6
Coefficient: we can't generally say the coefficient of polynomial, we should say the coefficient of several times in multinomial. For example, the coefficient of quadratic term is 4a

How to calculate the monomial coefficient and times? Make it clear! OK, add 50 points
Ask the coefficient and times of the following questions. Tell the reason... Just don't understand. Ask the teacher many times don't understand
5ab² , 1/3 a²b² , -7xy² , -a , -3²x²y
4 π x (π is pie), - 4 × 10 & # 179; a to the fourth power
-7/3
There is one question that I think is the most difficult, but I can't
3a²b³
-------
five
(the one above is a fraction. 3A & # 178; B & # 179; / 5)
If you can make me understand completely, add another 50 points
It's better to be more popular

For example: (1) 2x / 3 = (2 / 3) · x, then the coefficient of 2x / 3 is 2 / 3; (2) 4 π R & # 179; (3) = (4 π / 3) · R & # 179;, then the coefficient of the formula is 4 π / 3

The sum of monomials - 2x2y, - 12xy2, 2x2y, - XY2 is___ ．

The sum of the four monomials = - 2x2y + (- 12xy2) + 2x2y + (- XY2), = - 2x2y-12xy2 + 2x2y-xy2, = - 32xy2

How to calculate the number of times in a monomial

The sum of the exponents of all the letter factors, such as 3x & # 178; Y & # 178; Z, ∵ 2 + 2 + 1 = 5, ∵ is a binomial of degree 5