Question

does anyone know why y'=2x, y(0)=0, y(1)=100
has no solution?

Answer 1

If dy/dx = 2x, what is the general solution of that equation?

It's y(x) = x^2 + C.

Now is there ANY choice of the number C such that y(0) = 0 and y(1) = 100?

Answer 2

Ya general solution y=x^2 + c1 no problem. but the book says "Show that the problem has no solution. Is this an Initial value problem?" I don't how this statement can be correct when c can take on any value since it is arbitrary.

Answer 3

right you have a contradiction so there is no y with those conditions that satisfy the differential equation

Answer 4

Given that y(x) = x^2 + c, you now what to find ONE value of c such that it both true that

y(0) = 0

AND

y(1) = 100

Does there exist one value of c such that both of those conditions are satisfied?

Answer 5

nope

Answer 6

Therefore the initial value problem
y' = 2x, y(0) = 0, y(1) = 100
has no solution.

Answer 7

why does it have to be so opaque, but yet so simple.

Answer 8

it's not opaque now. That's why we do exercises! :-)