Hey all, i just lost a TON of points on a test for solving a(adsbygoogle = window.adsbygoogle || []).push({});

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 sorta 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!

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# (probably stupid) Differential equation question

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