Solving differential equations with undetermined coefficients y′′ + 3y′ + 2y = x y′′ − x^3 + 1 = 0

&The characteristic equation R ^ 2 + 3R + 2 = 0, & nbsp; obtains the characteristic root r = - 1, - 2, then the special solution y * = ax + B is set by the undetermined coefficient method and substituted into the differential equation to obtain 3A + 2aX + 2B = x, the solution a = 1 / 2, B = - 3 / 4

Given the parameter equation of differential equation, how to solve the differential equation
x=t^2+1
y=4/15t^5+c1t^2+c2
Is there a general method?

See Introduction to higher mathematics

Is it better to use the differential operator method or the undetermined coefficient method to find the special solution of the higher order non second linear differential equation with constant coefficients
When using differential operator, is it OK to set formula directly? Our teacher has given us four types of operator solutions, but will this be too few, or will the future topics not exceed these four types

We should be familiar with the properties of differential operators. As for the use of differential operators, we should be confident to use them boldly without going out of circles

The point (x, y) on y = - 5x + 6 of a function is above the X axis

To make the point above the x-axis, that is, to make y > 0
Find X

How do you read these
If a is alpha, B is beta

Greek letter a α alpha angle; coefficient b β beta flux coefficient; angle; coefficient Γ γ gamma conductance coefficient (lower case) Δ δ delta delta variation; density; diopter Ε ε epsilon epsilon logarithm base Ζ zeta zeta coefficient

Given a function y = root 5x + root 3, what is the value range of the independent variable x

Linear function y = √ 5x + √ 3
All of the first-order functions of the independent variable x
The range of values is any real number
The value range of the independent variable x in this problem is any real number

It is proved that: (1) if the series ∑ UN and ∑ VN converge and there is a positive integer n such that the inequality VN ≤ wn ≤ UN holds when n > N, then the series ∑ wn must converge
(2) If the series ∑ UN and ∑ VN diverge, and there is a positive integer n such that the inequality VN ≤ wn ≤ UN holds when n > N, is the series ∑ wn necessarily divergent?

Not necessarily. For example, UN = - / N, VN = 1 / n
Wn=1/n²

If the value range of the independent variable X of the linear function y = - 1.5x + 1 is - 2 ≥ X

-2 ≤ x < 4, then - 4 < - x ≤ 2, so - 6 < - 1.5x ≤ 3, then - 5 < - 1.5x + 1 ≤ 4, that is, y belongs to (- 5,4]
This kind of problem should be solved step by step, not step by step
I hope I can help you improve

Convergence of positive series UN, VN prove convergence of series (UN + VN) ^ 2 master!
Just a topic for postgraduate entrance examination and people who like mathematics
Let's learn from each other. What's the best topic to share

If the positive series UN converges, then UN converges to 0, that is, there exists n. when n > N, UN converges to 0

What is the value range of the function y = - 0.5x + 2?
Draw the image of function y = - 0.5x + 2

The value range of X is: ∞ x ∞
Image: first draw a coordinate, the midpoint is 0, and then point a few points: (0,2), (2,1) (4,0) to connect these points, and then extend them back and forth until you are satisfied. This is a straight line

Solving differential equations with undetermined coefficients y′′ + 3y′ + 2y = x y′′ − x^3 + 1 = 0