- #1
Jaevko
- 8
- 0
Hey all, i just lost a TON of points on a test for solving a
problem in a way that is apparently invalid.
The problem was verify that y(x) = x+1 is a solution for dy/dx =
y*y-x*x-2x; y(0) = 1. i plugged y = x+1 into the right side of
the second equation, got dy/dx = 1, integrated to get y=x+c, used
y(0) = 1 to get c= 1, therefore y = x + 1
My professor's annoyed 2-second explanation about why my method
is invalid was that I assumed that it worked to prove that it
worked. I sort of buy it, but I'm not completely convinced, could
someone give me a counter example to prove that my method is not
legit? [to clarify, my method is to plug in y(x) into the DE,
then integrate, then use the given initial conditions to solve for
c to get a new y(x) and make sure that my new y(x) is the same as
the old one].
The counter example I am requesting would take a form that is
similar to the problem above, except that y(x) would not be a
legit solution to dy/dx, BUT my method would falsely show that
y(x) does work. Obviously, if no such counter example exists,
that my method proves that the DE works and I should not have lost
any points
Thanks in advance!
problem in a way that is apparently invalid.
The problem was verify that y(x) = x+1 is a solution for dy/dx =
y*y-x*x-2x; y(0) = 1. i plugged y = x+1 into the right side of
the second equation, got dy/dx = 1, integrated to get y=x+c, used
y(0) = 1 to get c= 1, therefore y = x + 1
My professor's annoyed 2-second explanation about why my method
is invalid was that I assumed that it worked to prove that it
worked. I sort of buy it, but I'm not completely convinced, could
someone give me a counter example to prove that my method is not
legit? [to clarify, my method is to plug in y(x) into the DE,
then integrate, then use the given initial conditions to solve for
c to get a new y(x) and make sure that my new y(x) is the same as
the old one].
The counter example I am requesting would take a form that is
similar to the problem above, except that y(x) would not be a
legit solution to dy/dx, BUT my method would falsely show that
y(x) does work. Obviously, if no such counter example exists,
that my method proves that the DE works and I should not have lost
any points
Thanks in advance!