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Second Order ODE
- Thread starter MrJoe2000
- Start date
D
Deleted member 4993
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I'm stuck on this problem. Can someone show me how to get the answer?
d2x/d2= x
The answer the book is giving me is x = c1et+c2e-t Please Help meeee
As posted, your problem does not make sense! Please correct your typos. Please post the exact problem.
Do you know what is the characteristic equation of an ODE?
You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:
http://www.freemathhelp.com/forum/th...217#post322217
We can help - we only help after you have shown your work - or ask a specific question (not a statement like "Don't know any of these")
Please share your work with us indicating exactly where you are stuck - so that we may know where to begin to help you.
D
Deleted member 4993
Guest
My apologies. The problem should read:
d2x/dt2= x
How about rest of my directions. Which were:
Do you know what is the characteristic equation of an ODE?
If your textbook or class notes are absent, then for quick review go to:
http://en.wikipedia.org/wiki/Linear_differential_equation
You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:
http://www.freemathhelp.com/forum/th...217#post322217
We can help - we only help after you have shown your work - or ask a specific question (not a statement like "Don't know any of these")
Please share your work with us indicating exactly where you are stuck - so that we may know where to begin to help you.
Last edited by a moderator:
D
Deleted member 4993
Guest
I am not given any more information other than the equation I have stated. I'm asked to find the solution to that differential equation.
And I am asking:
Tell us what do you know about this type of ODE?
Where do we start? Do we need to start with definition and utility of ODE? Unless you show some work - we are totally in dark!!
D
Deleted member 4993
Guest
I'm totally in the dark as well. I know that I'm looking at this in the form of d2x/dt2 = Y ← No you are not!!
Your equation is:
d2x/dt2 = x
I know that dx'=xdt and if I then I multiply both sides by x' I get something but I dont understand how they get an answer in terms of x=?
Did you visit the web-site I had referred to?
Tell us what did you learn from there - particularly what is the characteristic equation of this type of ODE?
HallsofIvy
Elite Member
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- Jan 27, 2012
- Messages
- 7,760
Whoever gave you this problem clearly believes that you are taking or have taken an introductory course in "Ordinary Differential Equations". Is that true?
This is a "linear equation with constant coefficients". Do you know anything about those? One of the things you should have learned in Calculus, is that the derivative of \(\displaystyle e^{ax}\) is \(\displaystyle ae^{ax}\), its second derivative is \(\displaystyle a^2e^{ax}\), etc.. Since that also has "constant coefficients" for its derivatives, it would seem a good candidate. What do you get if you put \(\displaystyle y= e^{ax}\) into this equation?
This is a "linear equation with constant coefficients". Do you know anything about those? One of the things you should have learned in Calculus, is that the derivative of \(\displaystyle e^{ax}\) is \(\displaystyle ae^{ax}\), its second derivative is \(\displaystyle a^2e^{ax}\), etc.. Since that also has "constant coefficients" for its derivatives, it would seem a good candidate. What do you get if you put \(\displaystyle y= e^{ax}\) into this equation?