I just realised this is exactly how one may solve for the wave equation in quantum mechanics: by expanding the problem in terms of the eigenvectors of the operator.
Your eigenvalues are wrong, take that 2x2 matrix to be A, (I'm using &=lamda) then det(A-&I)= |5-& -3 | |-6 2-&|=0 =>(5-&)(2-&)- (-6*-3)=0 =>&^2-7&-18=0 which factorises to (*+2)(*-9)=0, and so our eigenvalues are &=-2 or &=9, not -1 and 8.
How shall we solve if there are constants added to the differential equations too? For example, equations like x(dot) = 5x - 3y + 10, and y(dot) = -6x + 2y - 3
Maths with Jay You are welcome and thanks again the video helped me. John 3:16 For God so loved the world he gave his only begotten son that whosoever believeth in him should not perish but have everlasting life. :)
I just realised this is exactly how one may solve for the wave equation in quantum mechanics: by expanding the problem in terms of the eigenvectors of the operator.
Brilliant! Thank you for letting us know.
For me it was given in context of birth-death process
Do you have example when the eigenvalue is identical?
What would you do if you had in the x (dot) equation a lets say + e^t along with the 5x - 3y?
Is it multiplying the 5x - 3y?
@@MathsWithJay no it is added with it
Your eigenvalues are wrong, take that 2x2 matrix to be A, (I'm using &=lamda)
then det(A-&I)=
|5-& -3 |
|-6 2-&|=0
=>(5-&)(2-&)- (-6*-3)=0
=>&^2-7&-18=0
which factorises to (*+2)(*-9)=0, and so our eigenvalues are &=-2 or &=9, not -1 and 8.
You have forgotten to multiply 5 and 2 to get 10. Then 10 - 18 = -8. See th-cam.com/video/tXlMbAxbUI4/w-d-xo.html for the whole calculation and check.
Maths with Jay ah yes of course
Please could you say how did you find λ ? Thank you.
I looked at this in an earlier video: th-cam.com/video/tXlMbAxbUI4/w-d-xo.html
this finally made me understand systems of ode, thank you!
You're welcome!
Thank you
It was all crystal clear
I watched 4 videos and none of them explained it as well as you
Thank you soooo much :))
You're very welcome!
@@MathsWithJay I got the question in my exam right
Thank you so much:)
That's excellent! Thank you for letting us know.
Thank you so much. This solution way very easily than other solution.
Glad it helped
How shall we solve if there are constants added to the differential equations too?
For example, equations like
x(dot) = 5x - 3y + 10, and
y(dot) = -6x + 2y - 3
To get 10....add 10t, so that when you differenttiate, you get 10
But how does this help. Now I have a solution with two new variables C and D. What does these two say?
This is the general solution...C and D are constants to be found with given conditions
How to find the values of c & d
@Arun: That would depend on initial conditions...we have not got this information here.
after checking the obtained solution the final expression we got is in terms of t, i couldnt understand
@Suraj P: The dot on top of the x means dx/dt. Similarly for y.
Awesome, great great great amazing wonderful awesome
@Marko Jurisic: Thank you so much!
would this still be applicable if the 2 differential equations are of different orders but in terms of the same variables ?
@Jason: What order?
@@MathsWithJay 2nd order?
will this work when one of the eqns has a const?
Where?
Thank you.
@Ali: Thank you!
When two eigen values are same then what to do
Does this help? tutorial.math.lamar.edu/classes/de/RepeatedEigenvalues.aspx
@@MathsWithJay thank you so much!!
Saviour!
Thank you!
This series was one of the clearest and best ever. Thanks very much.
Thank you!
Thank you God bless :) !
Many thanks!
Maths with Jay You are welcome and thanks again the video helped me.
John 3:16 For God so loved the world he gave his only begotten son that whosoever believeth in him should not perish but have everlasting life. :)
Great explanation. Thank you!!
Thank you so much
Why does every1 call the constants "arbitrary variable" i see absolutely no point in doing that.
An arbitrary constant is a constant which can be assumed to be anything, it doesn't have one fixed value like a general constant