Ivp help: y' = sqroot (y^2-9) , y(xo) = yo

[Ryan Rigdon]

Here is my problem

y' = sqroot (y^2-9) , y(xo) = yo has a unique solution.

Any helpful hints on how to get this started would be most helpful thank you

 

[HallsofIvy]

Here is my problem

y' = sqroot (y^2-9) , y(xo) = yo has a unique solution.

Any helpful hints on how to get this started would be most helpful thank you

That's obviously a separable equation: \(\displaystyle \frac{dy}{dx}= \sqrt{y^2- 9}\) becomes \(\displaystyle \frac{dy}{\sqrt{y^2- 9}}= dx\) and now integrate both side. Can you integrate \(\displaystyle \int \frac{dy}{\sqrt{y^2- 9}}\)? A trig substitution should do it- perhaps y= 3 sec(t).

 

[Ryan Rigdon]

solved will post findings after it has been turned in. thank you for the help.