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

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

sirm3d · Answer

$y'(0)$ is not defined

anonymous · Answer

how do you know that it is not defined?

dumbcow · Answer

based on your function of y

y(0) =0   not 1
?

sirm3d · Answer

$$y'=C_1+\frac{C_2}{2\sqrt x}$$

clearly, $y'(x)$ does not exist when $x=0$

anonymous · Answer

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