Question with solve block solution on a math problem

[ptc-4735478]

Please see the attached for the question.

Basically I would like to know the analytical solution to my differential equation.

And why would the solve block give different solution after a parameter, t, is changed (Given the same initial guess)

The strange things is it seems to be the solution of the two constant I am solving should not be dependent on t, so they should not change when I change t.

This is a case specific problem.

BTW, can someone tell me what is the general solution to the system of differential equation

x' = x+y

y' = x-y

is it exponential function or trig ? I have difficulties looking it up because I don't know what class of problem is this...please provide a keyword for me to research on it.

Thanks

Henry

[Werner_E]

You have three variables (A, B and t) and only two equations, so you may chose one of the three freely:

Lets assume a=1 and choose any A (A>1!!)

Then B=(2-A)/(A-1) and t=ln(A-1)*(A-1)/(2-A^2)

or B+1 = 1/(A-1) and t = ln(B+1)/(A-B) = ln(A-1)/(B-A)

So there is only a very limited range of t you can expect a solution.

Most solutions find finds are due to the tolerance set and are not solutions - e^At and e^Bt appear to be zero (which they aren't).

[AlanStevens]

henry leung wrote:

BTW, can someone tell me what is the general solution to the system of differential equation

x' = x+y

y' = x-y

Differentiate the first equation wrt t again: x`` = x` + y`. Substutute for y' from the second equation: x``=x`+x-y. Replace the y that remains from the first equation: x``=x`+x-(x`-x). This gives: x``=2x. You might find this easier to solve.

Alan