Solving a Difficult Equation After 20 Years: Tips and Tricks for Success

  • Thread starter jrbigfish
  • Start date
In summary, the conversation is about solving a polynomial equation using the quadratic formula and finding the general solution using the Euler's formula. The conversation also includes discussions on the roots of the characteristic equation and the use of the quadratic formula. There is also a mention of the underdamped solution and the correct form of the general solution.
  • #1
jrbigfish
7
0
I hope my posting is not against the rules.
The equation is not that difficult but I had being out of school for 20 years.

y"+2y'+4y=0 Then I do
r^2+2r+4=0
then you can not do
(r+2)(r+2)=0 because do not work. can I have some help please?
 
Physics news on Phys.org
  • #2
Welcome to PF!

Hi jrbigfish! Fishy welcome to PF! :smile:

(try using the X2 tag just above the Reply box :wink:)
jrbigfish said:
r^2+2r+4=0
then you can not do
(r+2)(r+2)=0 because do not work. can I have some help please?

use good ol' (-b ± √(b2 - 4ac))/2a …

in this case -1 ± i√3. :wink:
we need more fish! :biggrin:
 
  • #3
Most polynomial equations cannot be factored (with integer coefficients). Complete the square or use the quadratic formula.

Completing the square:
[itex]r^2+ 2r+ 4= r^2+ 2r+ 1- 1+ 4= r^2+ 2r+ 1+ 3= (r+1)^2+ 3= 0[/itex]

Quadratic formula:
[tex]r= \frac{-b\pm\sqrt{b^2- 4ac}}{2a}[/tex]
with a= 1, b= 2, c= 4.
 
  • #4
Ok the quadratic formula! Yes! But what is this roots of the characteristic equation are
r1,2=-a+/-(a^2-b)^1/2 what is this and when I use it?
 
  • #5
jrbigfish said:
Ok the quadratic formula! Yes! But what is this roots of the characteristic equation are
r1,2=-a+/-(a^2-b)^1/2 what is this and when I use it?

Do you mean r1,2 = -a ± √(a2 - b) ?

hmm :rolleyes: … that looks like the roots of x2 +2ax + b = 0.

I'd forget that formula if I were you.
 
  • #6
Ok thank you mag.
 
  • #7
Ok after I use the quadratic formula (-2+/-((12))^1/2)/2 which solves 0.732i and -2.73i. So the solution is of the form underdamped. So I use the equation y=e^(∝x) (C_1 cosβx+C_2 sinβx). then what?
 
  • #8
jrbigfish said:
Ok after I use the quadratic formula (-2+/-((12))^1/2)/2 which solves 0.732i and -2.73i.

(copy the ± and √ symbols)

Nooo … that's i(-1 ± √3) … you should have got -1 ± i√3. :redface:
 
  • #9
Ok -1 ± i√3 then what I do?
 
  • #10
jrbigfish said:
Ok -1 ± i√3 then what I do?

?? :confused:

you solve y' = (-1 ± i√3)y.
 
  • #11
so we end with y=Ce^(1±√3)t ?
 
  • #12
jrbigfish said:
so we end with y=Ce^(1±√3)t ?

what happened to i? :confused:
 
  • #13
so we end with y=Ce^(1±i√3)t ?? Help me here it has being 12 years after the B.S. is this correct?
 
  • #14
(try using the X2 tag just above the Reply box :wink:)
jrbigfish said:
so we end with y=Ce^(1±i√3)t ??

Sort of, but you won't get many marks if you write it like that.

e(1±i√3)t = ete±i√3t,

so the general solution is … ? :smile:
 
  • #15
Hi jrbigfish! Thanks for the PM. :smile:

The general solution will be Aetei√3t + Bete-i√3t

though it would be more usual (and much easier if the solutions are going to be real anyway) to write it in the form Aetcos√3t + Betsin√3t :wink:
 

1. What is an equation?

An equation is a mathematical statement that shows the relationship between two or more variables. It typically consists of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

2. How do I solve an equation?

To solve an equation, you need to isolate the variable you are solving for on one side of the equation. This can be done by using inverse operations, which means performing the opposite operation on both sides of the equation. For example, if the equation is 2x + 4 = 12, you would subtract 4 from both sides to get 2x = 8, and then divide both sides by 2 to get x = 4.

3. What are the different types of equations?

There are several types of equations, including linear equations, quadratic equations, exponential equations, and logarithmic equations. Each type has its own unique characteristics and methods for solving.

4. What are some common mistakes when solving equations?

Some common mistakes when solving equations include forgetting to perform an operation on both sides, making a sign error, and forgetting to distribute when necessary. It is also important to check your solutions to make sure they satisfy the original equation.

5. How can I get help with solving an equation?

If you are struggling with solving an equation, there are many resources available to help you. You can consult your textbook, ask a classmate or teacher for assistance, or seek help from a tutor or online resources. It is important to practice and seek clarification when needed to improve your equation solving skills.

Similar threads

Replies
8
Views
1K
  • Differential Equations
Replies
8
Views
485
Replies
1
Views
1K
  • Differential Equations
Replies
2
Views
685
  • Differential Equations
Replies
2
Views
917
  • Differential Equations
Replies
3
Views
1K
  • Differential Equations
Replies
4
Views
1K
  • Differential Equations
Replies
4
Views
2K
  • Differential Equations
Replies
4
Views
2K
  • Precalculus Mathematics Homework Help
Replies
1
Views
896
Back
Top