Question

Initial value:

Is there a member of the two-parameter family which satisfies the initial condition y(0)-1, y'(0)=2? If not, why not?

y=C(1)x+C(2)x^1/2

Answer 1

\(y'(0)\) is not defined

Answer 2

how do you know that it is not defined?

Answer 3

based on your function of y

y(0) =0 not 1
?

Answer 4

\[y'=C_1+\frac{C_2}{2\sqrt x}\]

clearly, \(y'(x)\) does not exist when \(x=0\)

Answer 5

thank you very much, i dont know why i didnt see x^-1/2 was 1/x^1/2. i knew that... thanks for the help!!! much appreciated